State tax filing
Yes, you file full-year for Kentucky. Your move was too short to have truly established residency in Ohio. Therefore, you are justified in claiming all of the income as a KY resident. However, since KY and OH are reciprocal states, you will only be taxed on your KY income. You can be refunded for all of the tax you paid to Ohio on your income.
You will file an OH nonresident return. On the return, you will see a screen entitled Reciprocity Wages. On that screen, you will input into the box the amount of wages reported on your W2 as Ohio wages. These will be excluded from your Ohio return, entitling you to a full refund. See the screenshot below on how to do this:
