I am in a similar situation and this is the answer I received from the Arizona Dept of Revenue:
Arizona nonresidents earning income from Arizona sources and who meet the filing threshold are required to file a nonresident tax return (AZ Form 140NR). Rental income from a property located in Arizona is considered income from Arizona sources. If you are required to file a nonresident return, report the rental income on Form 140NR, line 21.
Note: Arizona does not allow individuals a adjustment to reduce current year income with net a operating loss carry forward utilized on the federal return.
To determine if you meet the filing threshold for a nonresident see Form 140NR instructions, page 1) for the table listing the filing thresholds for each type of filing status.
It looks like the income threshold is $15,000, so it looks like you do not have to file if you did not collect rents beyond this amount. Hope this helps!
