A rash of animal shootings by police officers nationwide has law-enforcement agencies running for cover amid growing public outrage that could force state legislatures to require greater accountability from men and women in uniform. Police in Utah shot a family’s dog while searching for a lost boy, prompting hundreds of pet owners to protest June 28 in front of the Salt Lake City Police Department headquarters. They carried signs demanding “justice for Geist,” a 110-pound Weimaraner shot by a city cop within the dog’s fenced-in back yard. The “missing” boy was later found sleeping in his home. State police in...