If you didn't live in the state and you didn't work in the state, you normally wouldn't have to file a tax return,but in your case if there was withholding to that state, you would file a nonresident state return, and report that none of your income came from working in that state. You'll receive a refund, but it won't be sent to your resident state.
You would have to file a resident state return and pay tax on your income. If you respond with the specific states, I can possibly give you more information.
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