It depends.
If you literally moved your domicile (your main, primary home) back and forth, abandoning the old domicile with each move, then you would file a part-year resident return in each of the two states.
If you kept your domicile in State A all year, and moved to State B temporarily (for example, to attend school), then you would file as a resident of State A and a non-resident of State B.
If you kept your domicile in State A all year, and if State B has a "6-month rule", then you might have to file a resident return in each of the two states. (Many states regard you as a resident for tax purposes if you spend 183 days or more living in that state, even if your domicile is in another state.)
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
