It occurred in a single day between Sunday 15 September and Monday 16 September in Woodlands Park in Pickering.
A number of fence panels within the park have been broken.
A police spokesperson stated: “A full investigation is underway and we’re now urging anybody to return ahead with any info.
“Please e mail louise.neville-beck@northyorkshire.police.uk when you have any info that might assist our investigation.
“Alternatively, you’ll be able to name North Yorkshire Police on 101 and ask for Louise Neville-Beck, or contact Crimestoppers anonymously on 0800 555 111 or by way of their web site.
“Please quote reference quantity 12240168769 when passing info.”