Officers said Shamara Girod, 27, was run over at Heller Park at 53rd and Utica around midnight.
Police said someone put Girod into a car to take her to the hospital. That car ran a red light at 61st and Lewis and was hit by another vehicle, authorities say.
Police said they don't know if Girod died because of injuries from the crash or being run over at the park. They are awaiting the results of an autopsy by the state Medical Examiner's Office.
The other five people in the car with her, including three children, ages three, five and eight, were hurt. Police said the southbound driver who had the green light refused medical treatment.
Police said they'd been called to Heller Park at about midnight because of gunshots being fired. A few minutes later they got the call about the wreck at 61st and Lewis.
Authorities recovered a knife and multiple shell cases at the park. They are looking for a silver car believed to have run over the woman.
The 61st and Lewis intersection was closed for several hours because of the crash.