Yes, you do. TurboTax will complete part-year and/or nonresident state income tax returns based off of the W-2 state income information, generally boxes 15-17. 

• To ensure accurate calculations, we strongly recommend preparing your nonresident state return before you prepare any resident or part-year state returns. Click on  How do I file a nonresident state return?

• On the state income tax return preparation part of TurboTax, you will be asked to allocate income to a particular state. Click on How do I allocate (split) income for a part-year state return?

For additional information, click on How do I file a part-year state return?