The car park barrier at the Town Hall, in St Nicholas Street, was forced open and damaged in the early hours of June 25.
Extensive damage was caused to the barrier, as well as its electric motor.
And today (Wednesday), police have released footage showing a group of people who appear to vandalise the barrier, in a bid to track them down.
PC Liam Cromack, of Scarborough Police, said: "This mindless act has resulted in a significant amount of damage to a car park barrier, damage that will have to be repaired out of council funds.
"If you were involved or know who may have been, I would urge you to contact me straight away to assist the investigation."
Anyone with information that could assist the investigation is asked to contact police 101, quoting reference number 12170111927.