Ohio would first need to assess you for the deficiency/overpayment. If they've done that they may have a claim against your refund, as most state's can offset their assessed deficiencies that have been reduced to state tax judgments against such refunds. However, on balance, it seems unlikely they would do so at the stage you are probably at.
Evan A. Nielsen is licensed to practice law in California and handles federal tax matters throughout the U.S. The information provided here is for educational purposes only and is not intended as legal advice for a particular matter. This response does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult an attorney.