No, it does not seem that
Arizona requires this kind of form.
Click here for FAQs on Arizona filing requirements. You are correct that she will file as an Arizona resident. Since she moved to Arizona and has now
established residency there, she will continue to be an Arizona resident like
yourself wherever you may be stationed in the future because of Military Spouse
Rules (See attached FAQ):
https://ttlc.intuit.com/replies/3302300
If you are given PCS orders to another state and she begins to work in
that state, she will need to tell her employer that she is an Arizona resident
because of the MSRRA. She will only be
taxed in Arizona and you will not need to file additional state tax returns.
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