First, you owe tax in the state where you live, and in every state in which you work. So if you physically worked in another state from where you lived, you would normally owe tax to that state (there are exceptions for reciprocal states).
Second, if you really did have state tax withheld to the wrong state, the correct (and only) procedure is to file a state return for that state, and get your withholding refunded to you if you owed no tax.
The problem is that your employer has already sent the money to the wrong state, and the state won't give it back until you file a tax return showing that you don't owe it.
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