Ohio certainly has a lot of local income tax rates, from school district codes to JEDDs....how do you keep track of so much!?
Stay out of OH. Along with PA these states are Payroll Hell.
Ohio actually has a pretty good resource - You can get to it from this website
The link for municipal taxes will take you to the "Finder"
The finder provides access to data bases that provide tax information for municipal and school district taxes for all addresses in Ohio.
Other Ohio Resources providing general information are
The Ohio local tax site also has a tool for uploading addresses for both Municipal income tax and School District tax. You can upload everyone with an Ohio address and get results in 24-48 hours. We do this audit quarterly as a double check and it's free. It saves a lot of time in lieu of looking up every address one by one.
Here is the registration link: https://thefinder.tax.ohio.gov/streamlinesalestaxweb/User/SimpleRegistration.aspx?from=SchoolDist
Here is the instructions link: https://thefinder.tax.ohio.gov/streamlinesalestaxweb/Upload/UploadInstructions_SchoolDistrict.aspx
I also urge caution with deducting courtesy taxes. You are not always required to withhold a resident Municipal tax, but like so many other payroll taxes, the rules are not consistent from jurisdiction to jurisdiction.
I've always lived, worked, and processed payroll in Ohio (among many other states for processing payroll). To me, all of the Ohio local and school district taxes are the norm. I'm always surprised at how many other states don't have any local taxes! I guess it's all relative ;-)
CA has local and school taxes, on property tax bills. In my case, along with mosquito abatement district, 911/paramedic, community college, etc. The money has to come from somewhere, different places have different means of collection.