Staff Sgt. Jennifer Pound says the investigation shows that there was an argument between the suspect and the victim just before the man was run down.
The suspect was arrested and charged on Saturday, but the victim died the next day in hospital.
The suspect had faced four charges, including leaving the scene of a crash and aggravated assault.
But Pound says the original charges against the man have been stayed now that police are looking into murder allegations.
The victim has been identified as 41-year-old Dwayne McCormick.