North Yorkshire Police said several parked vehicles were damaged in the Clifton area overnight from Saturday, June 7 into the following morning.
A force spokesperson said at least six vehicles were vandalised, including smashed windows or offensive symbols scratched into paintwork.
They added: "Officers from York neighbourhood policing team have increased patrols in the affected area.
"Residents are being urged to check any dashcam, CCTV or video doorbell systems for signs of suspicious behaviour.
"If your vehicle has suffered damage, please report it to North Yorkshire Police.
"If you have information that could assist the ongoing investigation, please call 101, quoting reference number 12250103112.
"You can also speak to Crimestoppers anonymously on 0800 555 111."
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