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The Ohio Business Tax Guide (2008), on page 32, (Section: Municipal Income Tax, subsection: Tax Paid By)
Employers who are located in a municipality leving an income tax must withhold taxes from wages and salaries paid to employees, and can withhold taxes from wages and salaries paid to employees who reside in a municipality leving an income tax.
It seems to me that you are required to withhold taxes for the muncipality worked in, and may withhold taxes for the employees residence.
It goes on to say that the the Ohio Business Gateway, at http://obg.ohio.gov , has procedures you can use to simplify the process.