The incident happened just before 6 p.m. Sunday in Middlefield, The (Cleveland) Plain Dealer reported.
The officers pulled the suspect over, but before they could get out of their vehicle, the suspect allegedly got out of his car and started shooting, Geauga County Sheriff Daniel McClelland said.
One officer, a female, was shot in the hand, and the other, a male, was injured in the leg by fragments from the police car. The car had a shattered windshield, multiple bullet holes, was leaking fluid and had flat tires after the incident.
Both of the officers fired at the suspect and the man was fatally hit.
Names of those involved in the incident were withheld.