An Arizona monthtomonth lease agreement is a legally binding rental contract between landlord and tenant that renews every month. Find 6725 flexible and convenient short-term apartments for rent in Phoenix.All rentals will require, in addition, a security deposit equivalent to one (1) month's rent. a. An Arizona lease agreement is a document created for a landlord to outline the terms and conditions of renting property to a tenant. Talk to your property manager or owner and buy out your lease - or just ask to leave with next month's rent being theirs. Completed and signed application. Can my landlord tell me I have to be out of my apartment a month before my lease is up? Find a subletter: Try to find someone to move into your rental and take over the terms of your lease. Abide the Implied Warranty of Habitability. We process all applications using a scoring matrix and select the most qualified tenant based on that criteria.