A Vauxhall Astra police car was one of three vehicles involved in a crash on the A158 near the garden centre in Horncastle on Saturday.
A silver Toyota Yaris and Rover Mini were also involved in the crash, which was reported to Lincolnshire Police just after 11am on June 26.
The road was closed at the time and reopened at around 2pm on Saturday, but fortunately only minor injuries were reported, police said.
Lincolnshire Police are now investigating the circumstances of the collision.
Anyone who saw the collision, or who has dashcam footage, should contact police on 101 or via email at [email protected] quoting incident 165 of June 26.
Alternatively, it can be reported through the independent charity Crimestoppers anonymously on 0800 555 111 or online here.