It depends, but probably not. If no KY state tax was withheld (box 17 on your W2, where box 15 says KY), then the answer is no. (You do not file a KY return if there is local tax withheld in Box 19). Since KY and WV have a reciprocal agreement, you do not file a KY return in this case. This is the most likely scenario.
However, if you did have KY state taxes withheld, you would want to file a KY nonresident reciprocal return to have your KY state tax withholdings refunded to you. They would have been taken out of your check in error. You only pay WV state tax on your income.
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