You file a part-year resident return in each of the two states, and allocate your income between the two states according to your dates of residency. Here are TT's instructions for your situation:
How do I file a part-year state return? (intuit.com)
Your state tax obligations aren't determined by your withholdings; they're determined by the actual facts of your residency status. CAUTION: if you continued to physically work in State A after your move, your earnings after the move would be taxable by both State A and State B. That's because states can tax non-residents on income from work actually performed within their borders. In this circumstance you'd be able to claim a credit on State B's return for the taxes paid to State A on the double-taxed portion of your income.
Filing by mail and attaching a written explanation is optional; some taxpayers do, and some don't.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
