It happened in Low Road, Hellesdon, at around 8.10pm on Monday, December 22.
A blue Ford Fiesta was involved in a collision with a black BMW which failed to stop.
It was found abandoned a short time later in Earlham Grove.
Two people who had been travelling in the Fiesta suffered minor injuries and were checked over by the ambulance service.
Officers are keen to speak to anyone who witnessed the incident or has any footage of the manner of driving of either vehicle prior to the collision.
They should get in touch by calling 101 and quoting reference 472 of December 22.
Alternatively, they can contact CrimeStoppers anonymously on 0800 555 111.