The Mounties say the first incident happened on Oct. 1, when the cat's owner found it inside her home attempting to lick off duct tape.
In that incident, the owner was able to cut the tape off the cat and the animal wasn't harmed.
An RCMP news release says the same cat was targeted again this week sometime between Sunday night and Monday morning, when the cat did not return to the house.
The owner looked outside Monday morning and saw the cat with its tail taped to its back and tape on its paws, which a veterinarian removed after sedating the animal.
The Mounties say the family is extremely upset, and both the police and the SPCA are investigating.