If you were a part-year resident in two states during the year, you will split your income between those two states based on your time of residency in each. The income and taxes for each state will be prorated and a tax credit for taxes paid to another state will not apply.
Claiming a tax credit for taxes paid to another state is for the situation where you lived in one state, but had income from another (non-resident) state and were required to pay tax to the non-resident state. Then, you could claim a credit on your resident state return so that the income was not taxed by both states.
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