No, you did not answer anything incorrectly.
You can find your school district code based on where you live in Ohio.
The Ohio tax return requires a school district number even when you don't live in a community that has a school district tax.
The Ohio Department of Taxation provides a lookup tool that will find your school district code by entering your nine digit zip code.
To access Ohio's lookup tool visit https://thefinder.tax.ohio.gov/StreamlineSalesTaxWeb/ZipLookup/LookupByZip.aspx?taxType=taxsummary