Your wife may file her AZ tax return as either MFJ or MFS, her choice. She may file her AZ return as MFS even if you filed your federal return as MFJ. If she files MFS, remember that AZ is a community property state. That means that half her AZ income belongs to her and half belongs to you.
MN requires that you use the same filing status on your MN return that you used on your federal return.
https://www.revenue.state.mn.us/filing-status-individuals
**Answers are correct to the best of my ability but do not constitute tax or legal advice.