The event taken place in the Newby Crescent location at around 9.05pm on Friday, May 5.
Timmy the cat was discovered dead by a neighbour and it is thought he had actually been shot with an air rifle or pellet weapon.
North Yorkshire Police are appealing for details about anybody living in your area who owns an air rifle or pellet weapon, or anybody who remained in the location at the time and might have experienced the event.
If you can help the examination, you are prompted to email [email protected] or call 101, choose choice 2, and request for Jacob Higgins.
If you want to stay confidential, you can pass details to Crimestoppers by calling them on 0800 555 111.
Quote the North Yorkshire Police referral number 12230080606 when offering any information.