Q. I am unsure if I need to file for both states or only Ohio?
A. Only Ohio, because KY & OH are "reciprocal states". You will only need to file KY, to get a refund, if your employer mistakenly withholds KY tax*.
@DaveF1006 said: "you should file a Kentucky State tax return as a non-resident to receive a refund for the taxes withheld or receive a credit on your Ohio resident return for the taxes paid in Kentucky".
Because of the reciprocity agreement, Ohio will NOT give you a credit for tax paid to KY. The only way to get KY withholding back is to file for a refund from KY. KY has a specific form (740 NP-R ) for a reciprocal state refund. Rather than paying TurboTax for KY software, you should try filing that form by hand. It looks pretty simple.
https://revenue.ky.gov/Forms/740-NP-R.020521.pdf
As DaveF1006 said, you want to file the form ( Form 42A809 ) to ask your employer not to withhold KY tax.
*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.
If you are subject to Ohio School District Income Tax (SDIT), you can not get a credit, for KY local taxes withheld, on an SDIT return.
