The collision occurred on Thorpe Lane, Middleton involving a silver Renault Megane and red Nissan Qashqai at approximately 5.22pm on Sunday evening (July 3).
Two people suffered serious injuries and were taken to hospital for treatment.
Officers are appealing for anyone who witnessed the collision or either of the two vehicles as described above in the area prior to the collision to come forward.
Also, anyone who may have CCTV or dash cam footage, which could assist with the ongoing investigation, is asked to contact PC Walkin from Road Policing Unit via the 101LiveChat function on the website quoting reference 13220360378.