What exactly do you want expunged? Misdemeanor? Felony?
Here is the Ohio law on Expungement:
Ohio is a "sealing" state. Sealing allows first-time offenders to petition the court for the sealing of a conviction record. To be eligible, one must not have any current charges pending, or prior or subsequent criminal convictions, other than minor misdemeanors and those arising from the same incident. Completion of the court's sentence (fines, restitution, jail/prison, probation, etc.) and a waiting period from the date of discharge is also required (one year for misdemeanors or three years for felonies). Some serious offenses are ineligible.