Under Arizona's anti-deficiency laws, it should be non-recourse if all the following are true:
1. The property is 2.5 acres or less;
2. The property is limited to and used for one structure, which must be used as a dwelling (either a single one-family dweliing or a duplex); and
3. The refinancing loan only refinances "purchase money" of the property (meaning the original purchase price, plus original financing and closing costs, plus the refinancing costs). Because you are not taking any cash out, you would meet this third requirement if the loan you are refinancing was a "purchase money" loan (or you're refinancing a previous refinancing of a "purchase money" loan).
The third requirement applies only if the lender is foreclosing in court through a judicical foreclosure proceeding. If the lender is foreclosing via a trustee sale, then you only have to satisfy the first two requirements.
I hope that helps.
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