Check your W-2 for whether OH or KY is in box 15. In the personal info
section, of TurboTax, when it asks if you made money in another state, answer no, per the
reciprocal state instructions on that screen.
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 KY return every year.
However the reciprocity
agreement does not apply to local city or county taxes. You can not
get those refunded, but if you live in an Ohio city with a tax, they may give you a
credit or partial credit. Many do. You
need to check with your city.
