Filing KY return when living in Ohio?

Yes.  You will file a Nonresident Reciprocal Return with Kentucky to have KY state taxes withheld (Box 17). 

However, if the taxes are only in Box 19, then you do not file a KY return.  While state taxes are covered and only taxed in your resident state of Ohio because of the reciprocal agreement, local taxes are not covered by this agreement and will not be refunded on a Kentucky return, although your Ohio locality might allow you a credit for the out-of-locality taxes you are paying in Kentucky.

Q. Do I need to file a KY return along with my Ohio return?

A.  Yes, but read on for details.

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.

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

If you decide to use that form, in the personal info section, when it asks if you made money in another state, answer NO, per the reciprocal state instructions, on that page. This will prevent TurboTax from thinking you need to file a KY return.

However the reciprocity agreement does not apply to KY local city or county taxes (box 19 of your W-2).  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.