If your mortgage is recourse loan, your bank may go after you. Say your outstanding mortgage is x, and the bank sells the defaulted property for amount of y, if x-y > 0, you may be liable the shortfall. State laws are different, not sure about AZ, I know there is no deciciency judgment in CA. The chance that the bank will sue for deficiency is slim, it takes time and money for them to pursuit. If I were you, I will try to do deed in lieu of foreclosure first.
Good luck.