The theft of the plaque and damage to the signs around the walk near the pond on Maltongate in Thornton-le-Dale happened between Saturday and Monday.
"This area is enjoyed by the community and visitors but there are ongoing problems with antisocial behaviour and damage which will not be tolerated," said North Yorkshire Police on social media.
Anyone with information that might help with the police's investigation should contact North Yorkshire Police on 101, select option two, and ask for Louise Neville-Beck. You can also email [email protected], quoting police reference numbers 12210096537 and 12210096531.
Information can also be passed on anonymously via Crimestoppers on 0800 555111.