I moved out of Arizona to California in December 2020 and converted my old Arizona house to a rental property.
Personally, I would not bother with this for the 2020 taxes for several reasons.
1) We're talking less than a month. So the way the IRS does things, at best you'll get 15 days of depreciation.
2) There was no rental income in 2020
So I would wait until next year when doing the 2021 taxes and convert the property from personal use to rental property with a conversion date and an in service date of 1/1/2021.
It seems like the loss could be taxable in AZ
You got that backwards. You don't pay taxes on losses. You pay taxes on gains, and if there's a mortgage on the property, then it's not common at all for residential rental real estate to actually have any taxable gain each and every year it's classified as a rental.
Also, more than likely AZ does not qualify as your resident state for 2020 - not even as a part year resident based on what I read in the first paragraph at https://azdor.gov/sites/default/files/PROCEDURES_INDIV_1992_itp92-1.pdf
