It occurred at around 8.40pm on Saturday 10 August 2013, when a group of men damaged benches on a grassed area of Montpellier Hill.
Members of the public challenged their behaviour, which resulted in a scuffle.
Two men aged 22 and 23, from Harrogate were arrested on suspicion of affray. They have now been released on bail to allow for further police enquiries.
PC David Minto, of Harrogate Safer Neighbourhood Team, said:
This kind of behaviour is wholly unacceptable and not something we will tolerate.
If you were in the Montpellier Hill area at the time the damage occurred or witnessed the disturbance I ask you to come forward and contact the police straight away.
Anyone who can assist with this enquiry is asked to contact Harrogate police on 101, select option 2 and ask for David Minto. Alternatively information can be emailed to firstname.lastname@example.org