The smash happened on Saturday at about 6.10pm on Castlefields Way in Madeley.
It involved a Volkswagen (VW) Polo and a police vehicle which was responding to an emergency call at the time.
Extensive damage was caused to both vehicles, although no one was injured in the crash.
West Mercia Police are appealing for witnesses, in particular the drivers of a dark-coloured VW Gold Estate and a silver Vauxhall Corsa which were travelling from the direction of Aqueduct towards Madeley.
Anyone with information can contact police on 101, quoting incident reference number 463_I of November 21, 2020 or go to westmercia.police.uk
Alternatively, information can be passed anonymously through Crimestoppers at 0800555111 or crimestoppers-uk.org