Yes, you can file a joint federal return and file separate returns in both Arizona and California, provided the the non-resident spouse did not have any source income from the non-resident state.
Arizona and California are both community property states. What this means is that if your file separately, because in both cases the non-resident spouse lives in a community property state you will each have to claim 100% of the income you earned plus 50% of your spouses income. Because of the differences in tax rates and tax brackets, I doubt you would receive any benefit from filing separately. That said, the only way to be sure would be to prepare tax returns both ways and compare the total tax liability for each method.
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