The law in Ohio varies by jurisdiction. Most states are in the process of making hands free devices manditory, although none of them have banned cell phones in cars outright. While there isn't any hard evidence that driving while talking on a cell phone inhibits your driving, there is no need to take the chance of causing an accident with the hands free options that are available.
Here is a current list of states and jurisdictional laws around hands free driving with a cell phone:
http://www.ghsa.org/html/stateinfo/laws/cellphone_laws.html

