You will need to file both states. Kentucky and Michigan are reciprocal states. You are only taxed in your home state (KY) for this income. Since Michigan withheld tax, you will need to file a Michigan nonresident return with zero income. The screenshot below will show the screen where to do this on the Michigan return.
Save that refund, however, because all of the income you earned in Michigan will be taxed in Kentucky, so it is likely you will need the refund to pay on the amount you owe Kentucky.
Going forward, if you are still living in KY and working in MI, you may file a form with your employer so they take out KY tax instead of MI tax. Here is an FAQ that provides more information, as well as the form you need to file: https://ttlc.intuit.com/replies/4776822
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