And in a separate incident yesterday, June 30, Lancaster City Council's Dog Warden returned to their vehicle to find it had been vandalised.
Lancaster City Council is also appealing for information as to the identity of the culprit.
A police spokesman described the attack on the police car as "senseless" and has appealed for information in finding those responsible.
Lancaster Police said: "Whilst our officers were attending an incident on the Vale Estate in Lancaster one of our vehicles has been badly damaged, as such it has now been taken off the road for repair.
"Officers were attending a report of property being stolen on the estate and had to leave their vehicle in order to pursue a suspect.
"This is now one less vehicle that we have at our disposal, one less resource to search for a vulnerable missing person, to allow us to respond to a person in crisis, or a person is a victim of crime. Attacking emergency vehicles is nothing short of senseless, dangerous and an unnecessary cost to the tax payer.
"If you have any information which may assist us in identifying the individuals responsible for this please call us on 101, or you can all Crimestoppers, free an din confidence on 0800 555 111. Please quote log reference 0824/290620."
The incident occurred on June 28.
Lancaster City Council's Dog Warden service said: "Thank you to the vast majority of you who help support our service with your informed opinions and observations.
"But to the person who thought it fit to vandalise this van and put a member of staff at risk, shame on you!"