If there were state taxes withheld on the W-2, then you may need to file that state return to get a refund of those withholdings.
Otherwise, whether or not you need to file the non-resident return for the other state will depend on your filing status and the minimum filing requirements for that state.
TurboTax should give you some guidance along the way after you have entered all of your information. If you still have questions, you can share the state and your filing status here so someone can give you a more specific answer.
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