Employer withheld the wrong state taxes

I lived in Kentucky and worked in Ohio for the first three months of 2021 before moving out of state. My employer incorrectly withheld state taxes for Ohio when they should have withheld Kentucky state taxes.  Doing my KY returns, it looks like I haven't paid anything for the 3 months I lived there and worked in Cincinnati.  I understand KY/OH have a reciprocity agreement where I shouldn't have to pay OH state taxes (only local taxes for Cincinnati where I worked).

 

Questions:  What do I do for my Kentucky returns since nothing was withheld (guessing I just have to eat the full cost and underpayment penalty)?  What should I do or what do I need to file to get all of the incorrectly withheld OH state taxes refunded (example - would I file an OH state return as a non-resident with income of $0 to receive the refund of taxes, or is there a different form in TurboTax Premier CD product)?

I want to make sure I'm doing this correctly.