The collision happened near Monks Kirby, on the B4112 Rugby Road at the junction with Fosse Way at around 6pm on Sunday, May 8.
The two Vehicles involved were a silver Peugeot 5008 and a red VW Golf.
Three people suffered serious injuries during the incident, requiring them to be taken to hospital.
Police are now asking for any witnesses to come forward.
A spokesperson for Warwickshire Police said: “Enquiries are ongoing and officers would like to speak to anyone who was driving along the road at the time.
“They are also asking anyone who has information about the nature of the driving of both vehicles prior to the collision to get in touch.”
Anyone with information is asked to call Warwickshire Police on101, quoting incident 250 of May 8.