Yes, the reason you owe state tax this year is that you didn't have any state tax taken out of your 1099-R income. Since retirement income is taxed by OH, and you only had federal tax withheld, you will owe the state tax on the 1099-R income. If you have not yet reached the age of retirement in OH, you can't take the credit for retirement income, so you owe the state tax on the full amount that you included with your federal return. Now, if you are already at the age of retirement, you can take the OH credit, but it doesn't sound like you are. And the credit won't be as much as the tax even if you do qualify to take it.
What is your school district name and code? Some districts tax retirement income and some do not (they only tax earned income). But if you are in a district that includes retirement income, then that will definitely cause you to owe school tax also. Guide to Ohio’s School District Income Tax
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