A non-emergency services vehicle was seen driving with blue flashing lights on the A66.
It was seen between Brough and Penrith on Thursday at about 5.30am and at one point was in a layby.
Officers are asking for anyone with information, who may have seen a black vehicle with a male driver or who may have dashcam footage in the area at the time to contact them.
Anyone with information can report online at www.cumbria.police.uk/reportit, quoting incident 37 of December 30. You can also call 101.
Alternatively, you can contact Crimestoppers anonymously on 0800 555 111.
