718.01 (B) (2)
http://codes.ohio.gov/orc/718
It's not unusual for employers to take the easy way out and just withhold for all employees.
You'll need to file a non-resident city return to get a refund. It's a good idea to contact the city first, because they may require a special form for this situation, that is not in TT. My city calls it the itinerant employee refund form.
