QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT INVESTMENT COMPANY

Investment Company Act file number 811-7278

Nuveen Arizona Premium Income Municipal Fund, Inc.
(Exact name of registrant as specified in charter)

333 West Wacker Drive, Chicago, Illinois, 60606
Address of principal executive offices) (Zip code)

Jessica R. Droeger—Vice President and Secretary
333 West Wacker Drive, Chicago, Illinois, 60606
(Name and address of agent for service)

Registrant's telephone number, including area code: 312-917-7700

Date of fiscal year end: 07/31

Date of reporting period: 10/31/04

Form N-Q is to be used by management investment companies, other than small business investment companies registered on Form N-5 (§§ 239.24 and 274.5 of this chapter), to file reports with the Commission, not later than 60 days after the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use the information provided on Form N-Q in its regulatory, disclosure review, inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and the Commission will make this information public. A registrant is not required to respond to the collection of information contained in Form N-Q unless the Form displays a currently valid Office of Management and Budget (“OMB”) control number. Please direct comments concerning the accuracy of the information collection burden estimate and any suggestions for reducing the burden to the Secretary, Securities and Exchange Commission, 450 Fifth Street, NW, Washington, DC 20549-0609. The OMB has reviewed this collection of information under the clearance requirements of 44 U.S.C. § 3507.

Item 1. Schedule of Investments

Portfolio of Investments (Unaudited)
Nuveen Arizona Premium Income Municipal Fund, Inc. (NAZ)
October 31, 2004

	Principal		Optional Call		Market
	Amount (000)	Description⁽¹⁾	Provisions*	Ratings**	Value

		Consumer Staples - 1.3% (0.9% of Total Investments)

$	945	Puerto Rico, The Children's Trust Fund, Tobacco Settlement Asset-Backed Refunding Bonds, Series	5/12 at 100.00	BBB	$ 865,346
		2002, 5.375%, 5/15/33

		Education and Civic Organizations - 11.7% (6.6% of Total Investments)

	1,000	Arizona State University, Certificates of Participation, Series 2002, 5.375%, 7/01/19 - MBIA	7/12 at 100.00	AAA	1,115,110
		Insured

	1,000	Arizona State University, System Revenue Bonds, Series 2002, 5.000%, 7/01/25 - FGIC Insured	7/12 at 100.00	AAA	1,043,610

	1,250	Glendale Industrial Development Authority, Arizona, Revenue Bonds, Midwestern University, Series	5/11 at 101.00	A-	1,329,713
		2001A, 5.875%, 5/15/31

	1,050	Northern Arizona University, System Revenue Bonds, Series 2002, 5.000%, 6/01/34 - FGIC Insured	6/12 at 100.00	AAA	1,074,854

	1,400	Southern Arizona Capital Facilities Financing Corporation, Student Housing Revenue Bonds, La Aldea	9/12 at 100.00	AAA	1,465,968
		Project at the University of Arizona, Series 2002, 5.000%, 9/01/23 - MBIA Insured

	1,500	Tempe Industrial Development Authority, Arizona, Lease Revenue Bonds, Arizona State University	7/13 at 100.00	AAA	1,542,630
		Foundation Project, Series 2003, 5.000%, 7/01/34 - AMBAC Insured

		Healthcare - 15.9% (11.1% of Total Investments)

	2,000	Arizona Health Facilities Authority, Hospital System Revenue Bonds, Phoenix Children's Hospital,	11/09 at 100.00	Ba2	2,001,220
		Series 1999A, 6.125%, 11/15/22

	1,000	Arizona Health Facilities Authority, Hospital System Revenue Bonds, John C. Lincoln Health Network,	12/10 at 102.00	BBB	1,115,040
		Series 2000, 7.000%, 12/01/25

	800	Arizona Health Facilities Authority, Hospital Revenue Bonds, Catholic Healthcare West, Series	7/10 at 101.00	BBB+	885,560
		1999A, 6.625%, 7/01/20

	3,000	Mesa Industrial Development Authority, Arizona, Revenue Bonds, Discovery Health System, Series	1/10 at 101.00	AAA	3,331,200
		1999A, 5.750%, 1/01/25 - MBIA Insured

	515	Puerto Rico Industrial, Tourist, Educational, Medical and Environmental Control Facilities Financing	11/10 at 101.00	AA	585,328
		Authority, Hospital Revenue Bonds, Hospital de la Concepcion, Series 2000A, 6.375%, 11/15/15

	1,500	Scottsdale Industrial Development Authority, Arizona, Hospital Revenue Bonds, Scottsdale	12/11 at 101.00	A3	1,580,895
		Healthcare, Series 2001, 5.800%, 12/01/31

	1,055	Industrial Development Authority, Winslow, Arizona, Hospital Revenue Bonds, Winslow Memorial	6/08 at 101.00	N/R	802,982
		Hospital Project, Series 1998, 5.500%, 6/01/22

		Housing/Multifamily - 8.6% (6.0% of Total Investments)

	400	Phoenix Industrial Development Authority, Arizona, GNMA Collateralized Multifamily Housing Revenue	6/11 at 102.00	Aaa	421,692
		Bonds, Campaigne Place on Jackson, Series 2001, 5.700%, 6/20/31 (Alternative Minimum Tax)

	530	Phoenix Industrial Development Authority, Arizona, GNMA Collateralized Multifamily Housing Revenue	4/15 at 100.00	Aaa	530,000
		Bonds, Park Lee Apartments, Series 2004A, 5.050%, 4/20/44 (Alternative Minimum Tax) (WI, settling
		12/16/04)

	1,000	Phoenix Industrial Development Authority, Arizona, GNMA Collateralized Mortgage Loan Multifamily	9/10 at 103.00	Aaa	1,084,940
		Housing Revenue Bonds, Camelback Crossings Apartments Project, Series 2000, 6.350%, 9/20/35

	3,215	Tucson Industrial Development Authority, Arizona, Senior Living Facilities Revenue Bonds, Christian	7/10 at 101.00	AA	3,506,697
		Care Project, Series 2000A, 5.625%, 7/01/20 - RAAI Insured

		Housing/Single Family - 0.1% (0.0% of Total Investments)

	40	Phoenix Industrial Development Authority, Arizona, Statewide Single Family Mortgage Revenue Bonds,	6/05 at 102.00	AAA	41,366
		Series 1995, 6.150%, 6/01/08 (Alternative Minimum Tax)

		Industrials - 2.1% (1.5% of Total Investments)

	1,345	Yavapai County Industrial Development Authority, Arizona, Solid Waste Disposal Revenue Bonds, Waste	No Opt. Call	BBB	1,388,484
		Management Inc. Project, Series 2003B, 4.450%, 3/01/28 (Alternative Minimum Tax) (Mandatory put
		3/01/08)

		Long-Term Care - 0.6% (0.4% of Total Investments)

	345	Mohave County Industrial Development Authority, Arizona, GNMA Collateralized Healthcare Revenue	5/06 at 103.00	AAA	363,344
		Refunding Bonds, Chris Ridge and Silver Village Projects, Series 1996, 6.375%, 11/01/31

		Tax Obligation/General - 4.0% (2.8% of Total Investments)

	1,525	Maricopa County Union High School District 210, Phoenix, Arizona, General Obligation Bonds, Series	7/14 at 100.00	AAA	1,641,800
		2004A, 5.000%, 7/01/21 - FSA Insured

	500	Puerto Rico, Public Improvement General Obligation Bonds, Series 2002A, 5.500%, 7/01/19 - FGIC	No Opt. Call	AAA	592,725
		Insured

	330	Puerto Rico, Public Improvement General Obligation Bonds, Series 2001A, 5.375%, 7/01/28	7/11 at 100.00	A-	347,200

		Tax Obligation/Limited - 52.7% (36.8% of Total Investments)

	1,985	Arizona School Facilities Board, State School Improvement Revenue Bonds, Series 2003, 5.000%,	7/13 at 100.00	AAA	2,129,905
		7/01/21

	2,000	Arizona School Facilities Board, Certificates of Participation, Series 2004A, 5.750%, 7/01/18 -	7/14 at 100.00	AAA	2,328,060
		AMBAC Insured

	2,000	Arizona State Transportation Board, Subordinate Highway Revenue Bonds, Series 2004B, 5.000%,	7/14 at 100.00	AA	2,139,940
		7/01/22

		Arizona Tourism and Sports Authority, Tax Revenue Bonds, Multipurpose Stadium Facility Project,
		Series 2003A:
	3,000	5.375%, 7/01/20 - MBIA Insured	7/13 at 100.00	Aaa	3,319,290
	1,000	5.375%, 7/01/21 - MBIA Insured	7/13 at 100.00	Aaa	1,101,020

		Bullhead City, Arizona, Special Assessment Bonds, Parkway District Improvements, Series 1993:
	820	6.100%, 1/01/08	1/05 at 101.00	Baa2	832,948
	880	6.100%, 1/01/09	1/05 at 101.00	Baa2	893,455

	530	Estrella Mountain Ranch Community Facilities District, Goodyear, Arizona, Special Assessment Lien	7/10 at 102.00	N/R	588,300
		Bonds, Series 2001A, 7.875%, 7/01/25 (DD, Settling 11/10/04)
	575	Marana Municipal Property Corporation, Arizona, Revenue Bonds, Series 2003, 5.000%, 7/01/28 -	7/13 at 100.00	AAA	593,417
		AMBAC Insured

	3,400	Maricopa County Stadium District, Arizona, Revenue Refunding Bonds, Series 2002, 5.375%, 6/01/18 -	6/12 at 100.00	Aaa	3,822,756
		AMBAC Insured

		Phoenix Industrial Development Authority, Arizona, Government Office Lease Revenue Bonds, Capitol
		Mall LLC Project, Series 2000:
	1,000	5.375%, 9/15/22 - AMBAC Insured	9/10 at 100.00	AAA	1,106,460
	2,000	5.500%, 9/15/27 - AMBAC Insured	9/10 at 100.00	AAA	2,180,580

	2,150	Phoenix Civic Plaza Building Corporation, Arizona, Senior Lien Excise Tax Revenue Bonds, Series	7/05 at 101.00	AAA	2,229,400
		1994, 6.000%, 7/01/14

	2,000	Phoenix Civic Improvement Corporation, Arizona, Subordinate Lien Excise Tax Revenue Bonds, Series	7/13 at 100.00	AAA	2,138,420
		2003A, 5.000%, 7/01/21 - MBIA Insured

	1,200	Prescott Valley Municipal Property Corporation, Arizona, Municipal Facilities Revenue Bonds, Series 2003,	1/13 at 100.00	AAA	1,247,652
		5.000%, 1/01/27 - FGIC Insured

	1,000	Puerto Rico Public Buildings Authority, Guaranteed Government Facilities Revenue Refunding Bonds,	7/12 at 100.00	A-	1,045,390
		Series 2002D, 5.125%, 7/01/24

	805	Scottsdale Preserve Authority, Arizona, Excise Tax Revenue Bonds, Series 2004, 5.000%, 7/01/16 -	No Opt. Call	AAA	902,212
		FGIC Insured

	1,350	Tempe, Arizona, Excise Tax Revenue Bonds, Series 2004, 5.250%, 7/01/20 - AMBAC Insured	7/14 at 100.00	AAA	1,491,588

	500	Tucson, Arizona, Certificates of Participation, Series 2000, 5.700%, 7/01/20 - MBIA Insured	7/08 at 100.00	AAA	548,415

	1,100	Tucson, Arizona, Junior Lien Street and Highway User Revenue Bonds, Series 2000E, 5.000%, 7/01/18 -	7/10 at 100.00	AAA	1,192,235
		FGIC Insured

	2,300	Virgin Islands Public Finance Authority, Gross Receipts Taxes Loan Notes, Series 2003, 5.000%,	10/14 at 100.00	AA	2,350,462
		10/01/33 - RAAI Insured

		U.S. Guaranteed * - 16.7% (13.2% of Total Investments)**

	480	Puerto Rico, The Children's Trust Fund, Tobacco Settlement Asset-Backed Bonds, Series 2000,	7/10 at 100.00	AAA	523,877
		5.750%, 7/01/20 (Pre-refunded to 7/01/10)

	2,250	Maricopa County Industrial Development Authority, Arizona, Hospital Revenue Refunding Bonds,	No Opt. Call	AAA	2,891,925
		Samaritan Health Services, Series 1990A, 7.000%, 12/01/16 - MBIA Insured

	3,000	Mesa, Arizona, General Obligation Bonds, Series 1999, 5.000%, 7/01/18 (Pre-refunded to 7/01/09) -	7/09 at 100.00	AAA	3,314,040
		FGIC Insured

	2,000	Phoenix Civic Improvement Corporation, Arizona, Junior Lien Wastewater System Revenue Bonds, Series	7/10 at 101.00	AAA	2,344,180
		2000, 6.000%, 7/01/24 (Pre-refunded to 7/01/10) - FGIC Insured

	1,000	Puerto Rico Highway and Transportation Authority, Highway Revenue Bonds, Series 2000B, 6.500%,	7/10 at 101.00	A***	1,191,720
		7/01/27 (Pre-refunded to 7/01/10)

	500	Surprise Municipal Property Corporation, Arizona, Excise Tax Revenue Bonds, Series 2000, 5.700%,	7/09 at 101.00	AAA	572,070
		7/01/20 (Pre-refunded to 7/01/09) - FGIC Insured

		Utilities - 10.8% (7.5% of Total Investments)

	1,000	Arizona Power Authority, Special Obligation Power Resource Revenue Refunding Crossover Bonds,	No Opt. Call	AA	1,141,580
		Hoover Project, Series 2001, 5.250%, 10/01/15

	1,000	Coconino County, Arizona, Pollution Control Revenue Bonds, Nevada Power Company Project, Series	10/06 at 102.00	B-	1,012,530
		1996, 6.375%, 10/01/36 (Alternative Minimum Tax)

	1,075	Pima County Industrial Development Authority, Arizona, Lease Obligation Revenue Refunding Bonds,	1/05 at 101.50	AAA	1,135,523
		Tucson Electric Power Company, Series 1988A, 7.250%, 7/15/10 - FSA Insured

		Salt River Project Agricultural Improvement and Power District, Arizona, Electric System Revenue
		Refunding Bonds, Series 2002A:
	2,000	5.125%, 1/01/27	1/12 at 101.00	AA	2,103,840
	1,000	5.000%, 1/01/31	1/12 at 101.00	AA	1,030,710

	530	Salt River Project Agricultural Improvement and Power District, Arizona, Electric System Revenue	1/13 at 100.00	AA	562,998
		Bonds, Series 2002B, 5.000%, 1/01/22

		Water and Sewer - 19.0% (13.2% of Total Investments)

		Arizona Water Infrastructure Finance Authority, Water Quality Revenue Bonds, Series 2004A:
	1,825	5.000%, 10/01/19	10/14 at 100.00	AAA	1,995,893
	1,815	5.000%, 10/01/22	10/14 at 100.00	AAA	1,947,766

	1,005	Cottonwood, Arizona, Senior Lien Sewer Revenue Bonds, Series 2004, 5.000%, 7/01/24 - XLCA Insured	7/14 at 100.00	AAA	1,053,240

	3,500	Glendale, Arizona, Water and Sewer Revenue Bonds, Subordinate Lien, Series 2003, 5.000%, 7/01/28	7/13 at 100.00	AAA	3,623,024

	600	Oro Valley Municipal Property Corporation, Arizona, Senior Lien Water Revenue Bonds, Series 2003,	7/13 at 100.00	AAA	633,881
		5.000%, 7/01/23 - MBIA Insured

	1,250	Phoenix Civic Improvement Corporation, Arizona, Junior Lien Water System Revenue Refunding Bonds,	No Opt. Call	AAA	1,472,274
		Series 2001, 5.500%, 7/01/21 - FGIC Insured

	1,500	Phoenix Civic Improvement Corporation, Arizona, Junior Lien Water System Revenue Bonds, Series	7/12 at 100.00	AAA	1,556,490
		2002, 5.000%, 7/01/26 - FGIC Insured

$	86,170	Total Long-Term Investments (cost $87,537,365) - 143.5%			92,947,170

		Other Assets Less Liabilities - 2.8%			1,825,065

		Preferred Shares, at Liquidation Value - (46.3)%			(30,000,000)

		Net Assets Applicable to Common Shares - 100%			$64,772,235


(1)	All percentages shown in the Portfolio of Investments are based on net assets applicable to Common
	shares unless otherwise noted.
*	Optional Call Provisions: Dates (month and year) and prices of the earliest optional call or redemption.
	There may be other call provisions at varying prices at later dates.
**	Ratings: Using the higher of Standard & Poor's or Moody's rating.
***	Securities are backed by an escrow or trust containing sufficient U.S. Government or U.S. Government
	agency securities which ensures the timely payment of principal and interest. Such securities are normally
	considered to be equivalent to AAA rated securities.
N/R	Investment is not rated.
(DD)	Security purchased on a delayed delivery basis.
(WI)	Security purchased on a when-issued basis.


	Income Tax Information

	The following information is presented on an income tax basis. Differences between amounts for financial
	statement and federal income tax purposes are primarily due to timing differences in recognizing income
	on taxable market discount securities and timing differences in recognizing certain gains and losses on
	security transactions.

	At October 31, 2004, the cost of investments was $87,521,973.

	Gross unrealized appreciation and gross unrealized depreciation of investments at October 31, 2004,
	were as follows:


	Gross unrealized:
	Appreciation	$5,711,397
	Depreciation	(286,200)

	Net unrealized appreciation of investments	$5,425,197

Item 2. Controls and Procedures.

The registrant's principal executive and principal financial officers, or persons performing similar functions, have concluded that the registrant's disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940, as amended (the "1940 Act") (17 CFR 270.30a-3(c))) are effective, as of a date within 90 days of the filing date of this report that includes the disclosure required by this paragraph, based on their evaluation of the controls and procedures required by Rule 30a-3(b) under the 1940 Act (17 CFR 270.30a-3(b)) and Rule 13a-15(b) or 15d-15(b) under the Securities Exchange Act of 1934, (17 CFR 240.13a-15(b) or 240.15d-15(b)).
There were no changes in the registrant's internal control over financial reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR 270.30a-3(d)) that occurred during the registrant's last fiscal quarter that has materially affected, or is reasonably likely to materially affect, the registrant's internal control over financial reporting.

Item 3. Exhibits.

File as exhibits as part of this Form a separate certification for each principal executive officer and principal financial officer of the registrant as required by Rule 30a-2(a) under the Act (17 CFR 270.30a-2(a)), exactly as set forth below: EX-99 CERT Attached hereto.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant) Nuveen Arizona Premium Income Municipal Fund, Inc.

By (Signature and Title)* /s/ Jessica R. Droeger--Vice President and Secretary

Date 12/28/04

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed below by the following persons on behalf of the registrant and in the capacities and on the dates indicated.

By (Signature and Title)* /s/ Gifford R. Zimmerman--Chief Administrative Officer (Principal Executive Officer)

Date 12/28/04

By (Signature and Title)* /s/ Stephen D. Foy--Vice President and Controller (Principal Financial Officer)

Date 12/28/04

* Print the name and title of each signing officer under his or her signature.

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, DC 20549 FORM N-Q

QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT INVESTMENT COMPANY

SIGNATURES

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, DC 20549

FORM N-Q