The crash happened just after 7.30pm when Mirrabooka Detectives spotted a blue Holden Commodore on Mirrabooka Avenue with a stolen numberplate attached.
The detectives pulled the Commodore over on Boyare Avenue and were in the process of approaching it when the driver sped away.
The detectives jumped back in their car and attempted to stop the vehicle again but the driver failed to pull over.
Police said the Commodore turned onto Honeywell Boulevard and then onto Beach Road.
Moments later, the Commodore collided with a Ford Escape, causing it to roll.
It’s understood at the time of the crash police were seeking permission to pursue the vehicle.
Police said the offender failed to check on the occupants of the Ford, which included three adults and a two-year-old child, and was last seen running from the scene.
The detectives provided first aid to the occupants and additional police cars were called in to search for the offender.
A 39-year-old woman who was a passenger in the Escape was taken to Royal Perth Hospital for a head laceration.
The two-year-old child was not injured but was taken to Princess Margaret Hospital as a precaution.
The 31-year old female driver was taken to Sir Charles Gairdner Hospital to be checked over. The 36-year-old male passenger did not receive any serious injuries.
Police said inquiries are continuing into the identity of the person who was driving the blue Holden Commodore, which has been seized.
Anyone with information should call Crime Stoppers on 1800 333 000.