The reciprocity rule does not apply in your case. It's only applicable if you were a full year resident of KY. That is, line 12, of Schedule A, is not used , in your case.
You file a part year resident KY return and pay tax on your income up until the day your moved.
You also file a part year resident OH return.
Ohio does a convoluted tax calculation for non-residents/part year residents. It calculates tax on total income, then it calculates a non resident/part year resident credit, which it subtracts from the tax it calculated on the total income. The credit is calculated as your non-Ohio income divided by Total adjusted Income multiplied by the total tax. TurboTax (TT) does this by allocating your income as either Ohio or non-Ohio. W-2 income is normally allocated by the state name abbreviation shown in box 15 of your W-2. Because all your wages were earned in OH, your wages are all OH income even though your W-2 may say it's KY income (or some of it is KY income).* TT will ask you, item by item, in the state section, how much of your other income is Ohio or non-Ohio income.
OH then gives you a 2nd credit (or partial credit) for the wage income also taxed by KY. That is, you will have credits on both line 28 (non resident credit) and line 33 (resident credit) of the Ohio Schedule of Credits.
*Also be advised that you will probably have to use a work around in TT. At the w-2 screen split the boxes 15-20 W-2 info into 2 lines. On the 1st line leave KY in box 15 but make box 16 blank or 0; leave the KY withholding in box 17. On the 2nd line put OH in box 15 and all the state wages amount in box 16; box 17 will show the OH withholding, if any.
