Tyres were slashed on 18 vehicles in the south of Aylesbury in a series of incidents over the course of four days.
The incidents of criminal damage occurred between Tuesday November 27 and Friday November 30.
Damaged vehicles were reported in Harvey Road, Kilner Road, Simpson Place, Lister Green and Treves Green.
Investigating officer PC Mike Cowdrey said: “I am appealing for anyone who has any information about the incidents or may have seen anyone acting suspiciously around vehicles to get in touch.
"I would like to ask residents to review any CCTV or dash cam footage to see if anything has been captured.
“If you believe you have information that could help with this investigation, please call 101 quoting reference number 43180364381.
"Alternatively, you can contact Crimestoppers anonymously on 0800 555 111.
“Incidents like this cause significant impact to the victims as they have to take time out of their day to get the tyre replaced and the related expense is considerable.
“It is possible that there are further incidents that have not yet been reported to us.
"If you have been a victim, I urge you to report this online or call the non-emergency number 101.”