CA does allow credit for taxes paid to another state -- where it does not allow credit is for "reverse credit " states/ situations. AZ is one of the states does allow credit to CA resident/entities when AZ allows credit.
In your particular case, I believe, AZ is not giving you credit on income earned in AZ because you will be taxed on that income in CA. You are paying taxes to AZ on your non-resident AZ return, right?
In such a case , you do your federal return first then do the non-resident state return ( AZ) and thereafter do the resident State ( CA ) --- TurboTax will pull the AZ taxes paid/incurred on to the CA form and give you the credit.
Do you need more specific help or is this sufficient
