In the days after the tragic shooting of Michael Brown in Ferguson, Mo., news programs ran video after video showing local police around the country armed with machine guns and driving heavily armored vehicles. The New York Times described a desert-khaki-painted MRAP -- for mine-resistant ambush protected vehicle -- sitting next to a snowplow in the municipal garage of Neenah, Wis. And a report from The Chronicle of Higher Education revealed that the University of Central Florida in Orlando owns a grenade launcher, retooled to fire tear-gas canisters.

MORE: Read the rest of the December issue.

Hundreds of communities and campuses across the country have been the recipient of hand-me-down military equipment, from machine guns and armored vehicles to helicopters and night-vision goggles. All the equipment comes from the Department of Defense’s 1033 program, which gives police departments wartime gear that the military no longer needs.

Better that it’s shipped to local cops, the reasoning goes, than get tossed away. After all, local police surely can never be too prepared for the vast array of threats they face.

But the idea of an MRAP tooling around Wisconsin or a Humvee making the rounds on a college campus raises concerns among critics who question whether the feds are kindling racial tensions through a policy of super-arming cops. As Eastern Kentucky University criminal justice professor Peter Kraska told a reporter, a “small agency can go rapidly from one of protecting and serving to one of viewing the community as the enemy and a potential threat.”

That worry, in fact, led President Obama to call for a full review of the program. With Ferguson’s heavily armed cops tossing tear gas from behind armored vehicles, pundits suggested that the feds and their 1033 program had fueled the tensions on the city’s streets.

They were wrong. Almost none of Ferguson’s weaponry, as it turns out, came from the 1033 program. The town’s police department did pick up a couple of Humvees, a cargo trailer and a generator through the program, but nothing in the center of the controversy came from the Pentagon.

Ferguson and St. Louis police departments bought almost everything seen on television with their own money.

Most of the equipment in the program isn’t even weaponry -- Yale University received men’s trousers and Nashville’s police department got Zodiac boats, which its officers used in the 2010 floods to rescue stranded residents. With cops sometimes finding themselves not only in difficult tactical situations but also under assault, giving them the best protection makes sense. The real issue isn’t so much the feds fueling racial tension with the equipment, as it is that the equipment has come to symbolize ongoing frictions in many communities between local police and their citizens.

Many police departments have longstanding racial tensions with citizens, especially in those places where the composition of the police force doesn’t match that of the locality. In Ferguson, where two-thirds of the population is black, 50 of the 53 police officers are white. Ferguson isn’t alone. In nearby Grandview, the police force is 92 percent white while the population is 55 percent nonwhite. Kansas City, Kan., is doing a bit better. Its police department is 72 percent white while its population is 60 percent nonwhite.

Virtually all of these officers, it should be said, are incredibly dedicated and go to work every day facing a very tough mission. Diversity is much more complex than a numbers game, and some diverse departments have their own struggles with community relations. But with so many cities demonstrating the effectiveness of community policing, a racial gap between officers on the force and citizens on the streets can vastly complicate the community connection. As one black Ohio resident told a reporter about the non-black cops he encountered, “The police come here, they do their jobs, they don’t try to get to know anybody.” And, he continued, “The police don’t wave.”

Cops who connect with the communities they serve, criminal justice experts believe, prove more effective in building relationships, generating trust and de-escalating conflicts.

There isn’t good evidence on whether racial diversity makes police forces more effective, or whether police officers of different races treat the people they encounter any differently. Moreover, hiring more black officers doesn’t wipe away police-community tensions, and increasing diversity is a hard road, experts say. It seems to matter much more whether top officials support efforts by their officers to build neighborhood ties.

It’s easy to point to video of heavily armed cops as the cause of the racial problem, with the Pentagon driving a top-down racial wedge into local communities. That’s wrong.

Far more important is the bottom-up effort to strengthen the relationship between police officers and the citizens they serve. The way in which cops and communities connect has become one of the most important front lines in the continuing struggle over civil rights. Federally delivered MRAPs aren’t so much the cause of the problem as they are a powerful symbol that a great deal of work still needs to be done to make that connection.