Police said he fled in the car but was spotted by a patrol vehicle on Lord Street in Bassendean.
A pursuit ensued after he failed to stop, which ended when he rammed an unmarked police car after becoming trapped in a cul-de-sac in Morley and crashed into a low fence at a park, police said.
The teenager has been charged with six offences including assault, reckless driving, stealing a motor vehicle and assault to prevent arrest.
Police said the vehicle was stolen from a home in Salter Point early yesterday morning. The woman is in hospital with a serious head injury.