The force has received reports of offensive graffiti being seen in the areas of Orchard Fields, County Bridge and Riverside Walk.
Officers are requesting the public’s assistance to help establish the full circumstances surrounding the incidents and are asking anyone who may have seen anything suspicious in the areas to contact them.
They would also appeal to residents in the area to continue reporting any further incidents.
A North Yorkshire Police spokesperson said: “This type of crime is completely unacceptable and can have a huge emotional impact on its victims and the community as a whole.
“We are taking this incident very seriously and will not condone this type of behaviour, which is completely at odds with the welcoming nature of our local communities.”
Anyone with information which could assist the investigation is asked to contact North Yorkshire Police on 101, select option 2, and ask for Police community support officer Abi Moriarty or email [email protected]If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
Please quote the North Yorkshire Police reference number 12210195011.