Hartman was driving home to South Australia last Sunday and clipped a parked car in St. Peters.
However he failed to stop and instead kept on driving before reporting the incident to police in Murray Bridge the following day.
Police have since charged Hartman in yet another car-related incident for the Cats after Billie Smedst was criticised for taking a selfie while apparently driving at Christmas time last year.
"We are disappointed and frustrated that Brad has been involved in this incident and believe there have been too many motoring related issues with our players in recent years," Geelong CEO Brian Cook said.
"Brad should have handled this differently by stopping and then providing his details at the time.
"As a club it is clear that we need to reassess the manner in which we work with our players around their responsibilities as representatives of the Geelong Football Club. We will convene in the new year when the key people return to the club to develop a way forward in regard to this.
"The club has advised the relevant internal and external parties of the details of this incident."