You file both a Kentucky and a Michigan return, but, since Kentucky and Michigan are reciprocal states, you will file a nonresident reciprocal return with Michigan to have all of the Michigan state taxes returned to you. However, Kentucky does tax all of this income, so you will be getting back the Michigan taxes in order to pay the Kentucky amount that will surely be due.
The reciprocal agreement basically states that when you work in one state but live in another, you pay tax where you live and not where you work. You can file a form with the Michigan employer (if the individual continues to work in Michigan) that will allow tax to be paid to Kentucky instead of Michigan. Here is an FAQ with helpful information on this: https://ttlc.intuit.com/replies/4776822
As far as the local tax is concerned, there is no worries in Kentucky because KY localities only tax you when you work there. As far as Michigan local taxes are concerned, please see this website: https://www.payroll-taxes.com/state-tax/michigan-counties. If work was not done in any of these localities, there may not be a Michigan local tax assessed. If there was, and none was withheld, then you will need to go to the website for the specific Michigan city to see how the city tax may be filed.
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