Without knowing more about your specific tax situation, your question cannot be answered with certainty. But, here is some general information to know about filing taxes for two states.
If you lived in one state and moved to another during the year, then you would file a part-year resident return for each state. The income taxed by each state would be allocated between the two according to the situation. There would be no credit for taxes paid to another state in that case because each state would only be taxing the income they are supposed to tax.
If you lived in one state and worked in another state, then the income that you earned in the non-resident state may be taxed by both the state where you worked and your resident state. This is where the credit for taxes paid to another state comes into account. Your resident state return would allow you to claim a credit for the taxes you had to pay to the non-resident state based on the income that was earned there. That would help to reduce the double-tax situation for your earnings.
In general, when you have this situation, complete your non-resident return first and TurboTax will pick up information from that return to help you complete the 'credit for taxes paid to another state' section.
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