The Ohio Instructions for Filing: Personal Income Tax and School District Income Tax include a list of the Ohio school districts which assess income tax for 2019 (indicated by bold font and an asterisk next to it). If you lived in (resided) or were domiciled in one of these school districts for all or part of the year, you are required to file a school district income tax return, Ohio Form SD 100.
If the school district reported on your Form W-2 is not marked as having an income tax, you may need to consult with your employer to determine if the correct school district is listed on your Form W-2. It could also be possible that your employer is reporting Ohio locality tax withheld instead of school district tax withholding.
Also available is the Ohio Department of Taxation The Finder website which can help determine whether you are required to file Form SD 100 School District Income Tax Return. You can file Form SD-100 with TaxAct.