Tiny Hydro, Okla., decided last year it could no longer afford to pay a dog catcher, and put the police in charge. The two-officer force, wearing two hats, now finds itself at the center of a controversy.

Last month, Edwin Fry, 73 years old, used a pair of bolt cutters to spring his impounded poodle. The police picked up Mr. Fry and the poodle, Buddy Tough, as they fled on a riding mower. The officers, who were doing double duty as animal-control workers, put Mr. Fry in jail—and put Buddy down.

Outraged...