I live in Kentucky, refund was rejected for KY but accepted for Ohio because I work in Ohio. I do not think I can claim refunds for both states. help?

Your Kentucky return got rejected because all of your wages are taxable by Kentucky, even if they were earned in Ohio. Ohio and Kentucky have a reciprocal agreement, which means that if you live in one of these states but work in the other, you'll typically only need to file a return for the state in which you live. In reciprocal states, you cannot claim a credit of taxes paid to another state. 

However, if you had Ohio withholding, then you would have to file an Ohio nonresident return to get a refund of taxes paid to Ohio and then owe Kentucky (your resident state) the tax on your wages. In your situation, you would not have a refund from your home state of Kentucky, as well as one from Ohio. 

If you got a refund of all your Ohio state withholding on your nonresident return, then you should only have to fix your Kentucky return to indicate that all of your Ohio income is taxable in their state. 

Lastly, please give Form WTH_IT4NR to your employer so that they stop withholding Ohio state income tax and withhold Kentucky state tax as required.