Toronto police Det.-Const. Tamara Lawrynowycz says the woman was supposed to be handing over the dog to a new owner and was given a leash and muzzle to get the pet ready.
But police allege she instead hung the dog with the leash while inside the Toronto Animal Services shelter's quarantine room, where the Shar-Pei was being held after it allegedly bit someone.
Investigators say she had already fled the scene by the time shelter staff came in and found the pup without vital signs.
Police say 50-year-old Rita Mueller of Bolton is wanted on charges of killing or injuring an animal, causing or permitting unnecessary pain and disobeying a court order.
They say she runs Scooby's Dog House and Rescue — an organization police say may no longer be in operation — and investigators say they fear she may own other animals whose safety could be at risk.
Lawrynowycz says the Ontario Society for the Prevention of Cruelty to Animals is "aware" of the rescue "from previous history."
She says Animal Services contacted police over the incident in December, but declined to comment on the delay.