A blue Peugeot and a grey Saab were in collision at around 10.35am on Saturday, January 7 on the westbound carriageway of the A120 in Wix.
No-one was injured.
Officers are looking to trace a grey BMW that was in the area at the time.
They are looking for anyone with who saw the incident or that has dashcam footage of it to come forward to assist in the investigation.
Anyone with any information is asked to contact Pc Grant Fryatt at the Stanway Road Policing Unit on 101.