This interview has been edited for clarity and length.

In communities across America, the relationship between the public and the police is deeply fractured, and researchers believe this can lead to more violent crime, and to fewer crimes being solved.

When the Urban Institute conducted a survey of residents in the highest-crime neighborhoods in six major cities, it found that only a quarter of respondents believe police act in accordance with the law, and half believe police suspect them of being criminals simply because of their race or ethnicity. Thirty-six percent of respondents said they would not give information to help police find a suspect.

Much of this breakdown of police legitimacy has been pinned on “over-policing” — the targeting of black and Hispanic communities with excessive stops, use of force, and arrests for minor infractions. But, increasingly, the law enforcement community is recognizing that “under-policing” — in which the most serious crimes often go unpunished — is equally important.

A recent investigation by The Trace and BuzzFeed News found evidence that the low arrest rate for shootings is partly due to inadequate investigation. Detectives said they were often stretched so thin that shootings with good leads fell to the wayside. And in many cities, staffing reports revealed that hundreds, even thousands, of assaults and robberies every year don’t get assigned a detective for follow-up. People interviewed in West Baltimore often connected the police’s frequent crackdowns on drug offenses to their failure to arrest the people who were shooting their family members and friends.

Earlier this month, the National Network for Safe Communities held a symposium at John Jay College of Criminal Justice in New York on reconciliation initiatives between the community and the police. Afterward, we caught up with David Kennedy, the director of the NNSC and a professor at the college, to talk about how police solving more shootings would help repair the relationship between the community and the police.

Sarah Ryley: Does the NNSC’s police-community reconciliation initiative address improving arrest rates for shootings as a means to improve the legitimacy of the police?

David Kennedy: It doesn’t yet. But it’s important. As the public’s perception of police legitimacy goes up, violent crime goes down. And that’s particularly true in what could be called “troubled neighborhoods.” You can have legitimacy problems that are caused both by under protection and by over enforcement. And, the research suggests that as legitimacy goes down, you get a whole range of really toxic dynamics. One is: People stop reporting. They stop cooperating. They may stop convicting if they serve on juries.

Subtler stuff is that general support for the law goes down. People’s willingness to engage in informal community activities around producing public safety, voluntary association — those sorts of things go down. People’s willingness to interfere in public disorderly situations — like your neighbors’ kids are misbehaving — goes down.

And some of the more recent research says political participation and voting goes down. So, the way of looking at it all is: People are less likely to act as citizens.

What can police departments do to make arrests in more shootings?

There seem to be three clusters of factors. One is departmental attitude and culture. It is the conviction that we are going to do a good job, and we’re not going to take the easy excuses that allow us to do a bad job.

Then there are the resource and tech issues. So, workload, training, how people get to be investigators, the maintenance and transmittal of institutional wisdom, and the forensic and the technology resources. No question that that matters.

And then there’s legitimacy and community relationships.

Police often complain that witnesses, and sometimes even the victims, won’t talk, making it harder for them to make arrests for shootings. They also say shootings are less likely to have witnesses because assailants can strike from far away. So, it would seem that, if shootings are less likely to have witnesses, investment in technology and forensics would be important. For example, my colleague just published a story on how the San Diego Police Department has been pulling DNA from shell casings. They’ve been getting matches off 30 percent of the casings.

I’m not buying anything about distance and that kind of thing. Mike Green, the head of the New York State Division of Criminal Justice Services, is one of those folks who totally does not buy the excuse, “If people don’t tell us what happened, we can’t solve it.” His summation, as a career homicide prosecutor, is that he’s never had a cooperative victim in a homicide case. It doesn’t mean you don’t get homicide convictions.

So, when I was talking about culture — that’s the kind of thing that people say that gives them an excuse for not succeeding. Places that succeed don’t play like that.

Agencies are often required to follow up on every domestic violence assault, but it’s perfectly standard to not even assign other types of nonfatal shootings. Why do you think police often treat domestic violence so differently from street violence?

So, let me leave you with this thought: The kind of gun violence that we’re talking about is not the kind of gun violence that gets a lot of public and political attention. What gets the public and political attention is the spree shootings, and school shootings, and the sorts of things that from time to time awaken public and political sentiment and lead to a set of policy prescriptions.

What we’re talking about is not that kind of gun violence. It’s the everyday, grinding, incredibly destructive, mostly urban, mostly minority community, mostly minority victim, gun violence that makes up 99 percent of the nonsuicide gun deaths in the country. And it does not have the same kind of advocacy.

It’s not going to be addressed, for the most part, with the statutory agenda, and with the rest of the gun control agenda. It’s going to be addressed by day-in, day-out organizational excellence, resources, the profound shifts that come when there are as many people looking at nonfatal shootings as there are in the Family Violence Unit.

It’s arguably the case that there’s a kind of community advocacy that’s emerging around this kind of gun violence that might look a little bit like the beginning of the domestic violence advocacy world of 50 years ago. But, until people either care about this stuff or are made to care about it, it’s not going to change.