I agree with rjs, you do not pay OH state tax exept for the days you physically work in OH. If you work even one day, in OH, you will then be required to file a non-resident OH return.
Ask you employer not to withhold either state or city income tax. Most OH employers know that they are not required to withhold OH state income tax in your situation. But, some think they are required to withhold city income tax. If that happens, you may have to file a city return to get a refund. Contact the city for a special refund form.
