The seeming surge in fatal shootings by police officers has become one of America’s most divisive issues in recent years. From Ferguson to Baton Rouge, from North Charleston to Minneapolis, from Charlotte to Chicago, communities have been rocked by protests and demonstrations after local police officers shot and killed people, many of them minorities, some completely unarmed. Images of some of the most egregious cases have shocked the national conscience.

As the former chief of internal affairs for the New York Police Department...