It's the only state that classifies a specific breed of animal vicious, but the measure, passed 27-5, would change that, The Columbus Dispatch reported.
Sen. Mark Wagoner, R-Toledo, says the existing classification discriminates against pit bulls.
"In doing so, it discourages responsible dog owners from complying with licensing requirements," Wagoner said. "Canine profiling is expensive, ineffective and infringes on property rights."
The classification under Ohio's 25-year-old law has also prompted the need for liability insurance, he said.
Under the Senate measure -- Senate changes still need House approval -- pit bulls wouldn't be classified as vicious automatically, but if a dog displayed behavior problems, it could be classified as a "nuisance," "dangerous" or "vicious." Penalties against owners of dogs placed in one of the three categories would range from fines to felony charges.
The "vicious" designation would apply for a dog that seriously injures or kills a person without provocation, and the dog would be seized and euthanized.