The notice from the ODT (Ohio Dept. of Taxation) usually explains the reason for the tax bill. For that much tax, it sounds like they calculated tax on your whole year income. Check to see that TurboTax did the nonresident credit allocation form.. IT NRC
https://tax.ohio.gov/static/forms/ohio_individual/generic/PIT_ITNRC.pdf
Look carefully. Ohio also has City income tax and School District Income tax. The bill may have been for one of those; although $650 seems like too much for "short employment in Ohio".
