Rory, aged four, returned to his owners’ home on Arundel Drive, Darlington on May 29 with a significant injury to his eye.
Vets determined he had been shot with a BB gun or air rifle, and sadly made the decision to put him to sleep.
Police are now appealing for anyone with more information to get in touch and help with their investigations.
A spokesperson from Durham Police said: “Police are appealing for information following the death of a cat shot with what is believed to be a BB gun or air rifle.
“Four-year-old Rory returned to his home on Arundel Drive, Darlington, on Saturday, May 29, with a significant eye injury.
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“He was taken to the vets, who confirmed he had been shot with an air weapon and that the pellet was still lodged in his eye.
“Sadly, Rory was put to sleep due to the severity of his injury.
“Anybody with any information relating to the incident is asked to contact Durham Police on 101, quoting incident number 99 of May 30.”