The chase started around 3 p.m. after officers stopped Anthony Deangelo Gooch, 21 for a seat belt violation.
Gooch, who was wanted on outstanding warrants for failure to appear in court, jumped out of the car and fled on foot.
Officers chased him through the woods, over fences and through several yards until he reached Wedgedale Drive.
According to a preliminary investigation, it appears that Gooch stumbled as he was running into the street and fell into the path of a patrol car driven by Officer D.P. Sexton.
Gooch's head struck the right front corner of Sexton's patrol car. Sexton was coming to assist officers and, according to witnesses, swerved in an attempt to avoid the collision.
Gooch is being treated at Duke University Hospital for injuries that do not appear to be life-threatening. Sexton was not injured.
The case is being investigated by the Police Department's Traffic Services Unit, which is standard procedure for any traffic accident involving an officer.