The incident occurred within the children’s play area at Barberry Close between 12am on Monday 30 July and 1pm on Wednesday 2 August 2012.
The picnic bench, which was located to the rear of the changing rooms, completely melted in the blaze.
PC Karl May said:
This incident is an attack on the local community and posed a real danger to the nearby changing rooms which, thankfully, escaped damage.
I am appealing to anyone with information that could help catch those responsible to get in touch as soon as possible.
If you can help the investigation please contact North Yorkshire Police on 101, select option 2, and ask for Karl May.
Information can also be passed anonymously to Crimestoppers by calling 0800 555 111.