“I raised my girls to trust police officers,” said Brittany Moore back in April. “That if they ever got lost, to find a police officer and they would help them. Now they don’t trust them.”

Moore spoke those words at the state capitol in Colorado, during a rally on behalf of legislation meant to reduce incidents in which police officers shoot family pets. Her testimony underscores a serious problem for anyone who supports good law enforcement (which everyone should).

Just as biased news reporting is not just bad journalism but also bad for journalism, because it undermines trust in the press, poor policing is bad for law enforcement because it undermines trust in law enforcement.

Moore’s German Shepherd, Ava, was shot in 2011 by an officer who claims the dog bared its teeth and lunged. Moore says otherwise. “The rawhide bone fell from Ava’s mouth and she made the most awful sound that I have ever heard, and then immediately fell to the ground. She tried to get up one last time, but her hind legs wouldn’t work because her spinal cord was severed. . . . Our golden retriever went over and was nudging Ava trying to help her. Ava fell back on the ground and laid there and died slowly. . . . I will never forget the sound of my daughter’s torturous cries that night.”

Unfortunately, Moore’s story is not unusual. Cases of cops shooting dogs happen with discouraging frequency. According to a Justice Department report, “in most police departments, the majority of shooting incidents involve animals, most frequently dogs.” The shootings happen despite the fact that “dogs are seldom dangerous,” rarely bite, and even when they do, “the overwhelming majority of dog bites are minor, causing either no injury at all or injuries so minor that no medical care is required.”

The trouble is that police officers all too often don’t understand dog behavior. As the report (“The Problem of Dog-Related Incidents and Encounters”) explains: “an approaching dog is almost always friendly. A dog who feels threatened will usually try to keep his distance.”

Yet because officers often don’t know that, you get situations such as the one a couple weeks ago in North Carolina, where a Mooresville police officer shot a dog being trained as a service animal after it wandered onto his property.

Then there was the case — reported the same day — in Leander, Texas: Police officers serving a warrant went to the wrong house, then shot the family pet, Vinny. Or another recent case in which a Los Angeles officer shot a dog outside the owner’s home for reasons “not immediately clear,” according to news accounts. Or another recent case in which a St. Louis police officer shot his partner (yes, really) while aiming at “what they said was an aggressive-looking dog.”

Aggressive-looking? That’s an awfully low standard for pulling a trigger, isn’t it?

There are two opportunities to address this issue: after an unnecessary shooting, or before one.

After-the-fact remedies include lawsuits — with all the attendant expense, turmoil, and negative publicity those can entail. (Brittany Moore has filed a federal lawsuit over the death of Ava.) Another remedy involves criminal prosecution. In December a Denver, Colo., police officer was charged with aggravated animal cruelty — a felony — after he shot a dog that had been restrained on a catch-pole.

Prosecutions are better than impunity, and they might send a message. But they represent a far-less-than-optimal solution.

The best answer is to train police officers on how to avoid shooting family dogs. That’s what Leander authorities did, bringing in trainer Jim Osorio after Vinny got shot. “I teach them dog behavior, types of aggression, how to approach dogs, and what types of tools are out there other than a firearm,” Osorio told Texas TV station KVUE.

Here in central Virginia, Henrico County trains officers on dog behavior through video, demonstrations, and instruction from animal-control officers. But not all departments around the state are so enlightened. So Virginia lawmakers should introduce a measure like the Dog Protection Act that passed in Colorado last year.

The measure stipulates that Colorado policy is “to prevent, wherever possible, the shooting of dogs by law enforcement officers.” It requires every officer to be trained in handling domestic animals. The training is provided by a webinar created by volunteers — including animal-welfare experts — that costs the state nothing. And the law requires officers to let pet owners or animal-control personnel “control or remove a dog from the immediate area in order to permit a local law enforcement officer to discharge his or her duties” whenever that is feasible.

David Balmer, a Colorado state lawmaker who co-sponsored the measure, says the key to winning passage was cooperating with law-enforcement agencies — rather than simply trying to ram a mandate down their throats.

“We met with sheriffs and police departments from across Colorado,” he says, “incorporating their suggestions into the early drafts of our bill. At the beginning, we faced stiff opposition from law enforcement. As we met with them over and over, they eventually dropped their opposition and began helping us write the bill.”

The Colorado bill would make a good model for the commonwealth — and, for that matter, the country. It would save some dogs’ lives. It would keep some departments from getting sued — and perhaps keep a couple more partners from getting shot. And it would increase people’s trust of the police they see on patrol. What’s not to like?