Withhold for Ohio only. Even if MA taxes the income (which they probably won't), they will give you a credit for the tax paid to OH.
Your separate question is, how do you file for 2020. You file as a part year resident of both states, paying tax on income prior to the move to MA and after the move to OH. This assumes the move is permanent and you do not maintain a domicile in MA.
For others reading this question, the answer is different if the employer's location is in New York, Pennsylvania, Nebraska, Delaware or New Jersey. For guidance see: http://www.journalofaccountancy.com/issues/2009/jun/20091371.html
