The state of Ohio taxes income at rates from .537% to 5.421%
Social Security Benefits are not taxed by the state of Ohio.
If you work in an Ohio municipality you may be levied an income tax, the tax rate can range from .4% to 3% of your income. If you receive a pension, disability or income from dividends or interest you are exempt from the local tax. You may be required to pay a school tax, of .25% to 2% of your income, this is not typical as about only 30% of residents have to pay this.
If you are a resident of Ohio you are required to pay Ohio state income tax on any income, no matter the source or place earned, you may be subject to credits depending on taxes paid in other jurisdictions. If you are a non-resident you only pay state income tax on income earned in Ohio.
You are considered a resident if you maintain a domicile in the state of Ohio. Being domiciled depends on the number of periods of contact in the state during the tax year, which is a calendar year for most people. Contact periods are considered being away from your home state abode and spending a part of two consecutive days in Ohio.