I am filing out an OH non-resident return for someone who had no OH income, was a non-resident, but OH tax was withheld on 1099-R. It looks like you calculate the OH tax on the federal AGI plus OH additions (such as other state's muni bonds) minus OH subtractions (such as social security), just as for a resident.
Then I went to Schedule D for the non resident credit where you enter the income earned outside OH (from the income reported in line 3) divided by the income earned in OH. This ratio is 1. I think the fraction on line 67 should be 1.0000 and the line 67 would be the same as the OH tax. However, the fill out PDF form available at