Even if you are living separately, you still are allowed to file a joint return. This may be advantageous in your situation anyways because if you file separately, community property law comes into play and your return becomes very complicated. (Both Arizona and California are Community Property states).
Because of your income situation, you may be required to file Arizona as a part-year resident, because you are a married couple filing jointly. (If you have the option to file as a full-year resident, do so. Since she does not have any income your tax return will not be adversely affected by claiming this status).
Since there is not California income, you shouldn't have to file a California return. But to make sure, you can prepare a California nonresident return (this is how California would require it). If your CA tax is $0, you willl not need to file CA. In TurboTax Online, you may check this and then delete the CA return with the following instructions: https://ttlc.intuit.com/replies/3301384