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State tax filing
Q. If I live in Ohio but work in Kentucky do I have to file state taxes for both?
A. No. Or more accurately: usually no.
Look at box 15 of your W-2. It should say OH. That means that the tax in box 17 was withheld for Ohio.
Ohio has a reciprocal agreement, on wages, with all neighboring states. No state taxes are withheld or due and you do not normally need to file a return for the other state (MI, PA, KY, WV, IN). But OH will tax you on your other state income.
If other state taxes are mistakenly withheld, you then have to file a return, for the other state, to get a refund. OH will not give you a credit. You should ask your employer to stop withholding so you don't have to file a (MI, PA, KY, WV, IN) return every year.
However the reciprocity agreement does not apply to local city and county taxes. Box 19 is for local withholding. Box 20 is the name of the city or county. You can not get the box 19 amount refunded. But if you live in an Ohio city with an income tax, they may give you a credit or partial credit. Many do. You need to check with your city.