TurboTax implies that I enter a "Box 20 Code." But TurboTax also clearly stated, "if a box is empty on the W2, leave it blank in TurboTax."
no, leave it blank
To find out if you live in a school district or city with an income tax enter your address at:
http://www.tax.ohio.gov/Individual/LocalTaxInformation.aspx
Direct to ZIP + 4: https://thefinder.tax.ohio.gov/StreamlineSalesTaxWeb/ZipLookup/LookupByZip.aspx?taxType=taxsummary