Yes. Your wife was an Arizona non-resident because she was in the state for a temporary and transitory purpose. Additionally, I’m assuming you did not go to Arizona and maintained a permanent joint residence in Texas (“she went to Arizona”) so she maintained her Texas residency.
In the state of Arizona, full-year resident or part-year resident individuals must file a tax return if they are married and filing jointly and gross income is greater than $25,900. For non-resident individuals, the threshold numbers above are prorated based on the individual's Arizona gross income to their federal adjusted gross income.
Without seeing your return, it’s not possible to say whether you are required to file. A zero balance due indicates no tax due. It’s possible you are still required to file with a $0. However, tax penalties are based on unpaid tax, so there would be no penalty for not filing a $0 balance return.
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