For the Ohio income tax rates, see
https://tax.ohio.gov/individual/resources/annual-tax-rates
In general, after subtracting personal and dependent exemptions, if an individual makes more than $40,500 per year, your Ohio income tax liability is normally at least $750, and if a married couple makes more than $67,500 per year, then your Ohio income tax liability is normally at least $1,500. Please check your draft Ohio state income tax return to be sure.
You can also see your tax liability in prior tax years by looking at your filed Ohio IT 1040 forms. See Question 9 for where this is shown in the tax forms.