Yes, you will file an AZ non-resident return. Otherwise, the state has no way of knowing you operated at a loss and 100% of the rents collected will be taxable by the state of AZ.
Note that it is *extremely* *rare* for rental income to ever actually show a taxable gain "on paper" when you do your taxes. When you add up the deductible rental expenses of mortgage interest, property taxes, and the depreciation you are required to take by law, that alone is usually enough to exceed your rental income for the year. Add to that the other deductible rental expenses you are allowed, and you're practically guaranteed to operate at a loss "on paper". But if you don't file a return with AZ showing "on paper" that you operated at a loss, then as far as the state is concerned, 100% of your rental income is taxable.
