No. IL Schedule CR does allow a credit for local tax paid in another state; but that is only for IL residents.
"A nonresident may not take a credit on Illinois Schedule CR".
Reference: Instructions for Schedule CR (<a rel="nofollow" target="_blank" href="
http://www.revenue.state.il.us/taxforms/IncmCurrentYear/Individual/IL-1040-Schedule-CR-Instr.pdf">ht...>)
PS. There are no "County" income taxes in Ohio. What you are paying quarterly is either City or School District Income Tax (or both).
