A police officer in Missouri shot and killed a blind and deaf dog this week ... and while the department's saying the cop feared contracting rabies -- the community's calling BS. Teddy -- a five-year-old, 13-pound shih tzu mix was killed in Sturgeon, Missouri after escaping his yard. The owner gave the dog some water and called the police ... who The Washington Post reports shot the dog twice within minutes of arriving. Check out the body cam footage ... little Teddy's running around the field -- away from the officer at first before turning around and moving toward him, though not seemingly in an aggressive way. The officer -- identified as Myron Woodson -- appears to give a half-hearted chase with a catch pole -- before whipping out his sidearm and firing the lethal shots. Teddy's owner -- a local man named Nick Hunter -- told WaPo he took in his late pet when Teddy was just a pup ... noting he had a loving personality and never posed a threat to anyone. Nick says he thinks Teddy and his other dog Gizmo escaped the outdoor kennel he put them in so he could go to dinner ... digging under the fence and running off. Hunter says when he spoke to the officer, he said he was worried the dog was a possibly injured stray so he put the animal down ... but, now the city's saying Officer Woodson feared the dog had rabies, and shot him to protect himself. The department cleared him of wrongdoing. A petition online already has several thousand signatures calling for the officer to lose his job ... and the Post reports many in the community plan to show up in force at the city aldermen meeting next week.