The girl, one of two passengers, died at the scene. A man was airlifted to hospital with serious injuries.
Officers want to speak to a third person believed to have been in the car at the time.
It is thought the car went the wrong way up a one-way street before hitting a bollard and crashing.
Witnesses reported seeing a man fleeing from the vehicle. A police helicopter involved in the search for him.
People affected by the damage to the shop were evacuated from the building and a structural engineer was called to make the scene safe.
The force has referred itself to the Independent Police Complaints Commission “in line with standard protocol”, a spokesman said.
“Anyone who witnessed the incident, or saw the Volkswagen Golf – which has a black bonnet and black roof – prior to the collision, is asked to contact police,” the force said.
IPCC Commissioner Carl Gumsley said: “Firstly, my thoughts and sympathies are with the family and friends of the young woman who has died.
“Clearly we are at the very early stages of this investigation; IPCC investigators were deployed to the scene shortly after this incident, attended post incident procedures and have begun to gather information to aid their enquiries.”