Story highlights Incident occurs in Prince George's County, Maryland

Police pursue a car driven away from a double shooting

The man driving the car exchanges gunfire with police

Police say they don't know if the man or police killed the girl

A 3-year-old girl died Saturday after a man and police engaged in a chase and gunbattle, said police in Prince George's County, Maryland.

Police spokesman Lt. Bill Alexander said police began pursuing the man early in the afternoon when he drove a Nissan Maxima away from the scene of a shooting in Temple Hills.

One of the wheels fell off the suspect's car and he stopped and exchanged gunfire with police, Alexander said.

The suspect kept driving but stopped again and traded gunfire with police a second time.

The man was killed in the second exchange, Alexander said. Inside the vehicle, police found the wounded 3-year-old, who later died, Alexander said.

Police said they don't know who fired the bullets that killed the man or the girl. CNN affiliate WJLA said police believe the man was the girl's father.

Two wounded people were found at the scene of the first shooting -- the 3-year-old's maternal grandfather and maternal great-grandmother, police said. They were in critical condition at hospitals, Alexander said.