LOS ANGELES >> When the police arrived, she was barricaded inside her apartment with her ex-girlfriend, threatening suicide, a gun in her hand.

“Let your hostage go,” one of the officers shouted.

It was the beginning of a seven-hour standoff that brought out the SWAT team and the fire department, cost the city of Los Angeles tens of thousands of dollars and could well have ended in lost lives.

But three years later, when two Los Angeles Police Department officers interviewed the woman, Shawn Baxendale, in prison, she told them the police could have handled the situation better. The use of the word “hostage” by the first officers at the scene, she told them, stunned her — her ex-girlfriend had insisted on staying and could have left at any time, she said — and it made her feel that she had no options left.

“At this point I’m thinking, there’s no going back,” Baxendale said.

The interview, recorded on videotape, is part of an unusual project started by the two officers, Detective Teresa Irvin and Officer Michael Baker, to gain insight into the mindset of people involved in potentially violent encounters with the police.

They hope the information gained from the interviews — they have conducted about 40 over the last four years — will help law enforcement officers, especially those who are the first to respond to a scene, learn to diffuse volatile moments rather than escalating them.

“Cops like to solve things right away,” said Baker, a senior negotiator with SWAT who in more than 25 years on the force has responded to hundreds of “barricade” situations, “but I think that attitude sometimes causes a response that isn’t appropriate.”

“Just the way you approach a situation verbally or with your body language can put people on the defensive,” Baker said. “It’s been my experience from talking to people that a lot of them get scared, and that’s why they react the way they do.”

The interview project began informally. In 2007, Irvin, a field supervisor with the department’s Mental Health Evaluation Unit who has been with the department 18 years, started following up on some cases, visiting people at their homes, in prison or psychiatric hospitals and asking them what led them to such drastic actions and how the police could have handled the situation better.

Although police officers held debriefings to discuss how operations were handled, Irvin said, “We were never going back and actually speaking to the subject. It was incredible, the amount of information they would actually provide to us.”

Irvin and Baker have been asked to speak about the project at law enforcement conferences and military training programs and have been contacted by police departments interested in doing similar interviews themselves. They are developing a training program for the LAPD.

The Los Angeles police respond to about 100 calls involving barricaded subjects each year. Often, alcoholism, drugs or mental illness are involved, and in some cases the person has had repeated contacts with the police. How officers respond and what they say when they first arrive at a scene is critical, Irvin and Baker said.

The interviews, they added, make clear that it is never a single event that leads people to such extreme actions, but the accumulation of many stresses.

“Everyone has a breaking point and that’s what happens in these situations,” said Baker, who added that Baxendale, the woman who barricaded herself in her apartment, “was basically not a bad person. She had a bad day.” (Baxendale served four years in prison for criminal threats and negligent discharge of a weapon, but now has a successful business.)

In conducting the interviews, she said, she and Baker arrive unannounced and ask if the subjects will participate. The questions are unscripted.

But they always include asking how well the officers who first responded handled the situation, and what could have been done better. In cases involving barricades, they ask: “Why didn’t you come out? What could have caused you to come out sooner? Did someone say something that caused you to stay inside?”

So far, the only person who has refused to be videotaped, Irvin and Baker said, is Joseph Moshe, a man who in 2009 allegedly made threats against the White House and then drove to the federal building in West Los Angeles, where SWAT officers pumped so much tear gas into his car that the fire department had to hose him down afterwards.

But Moshe, who at the time was in a psychiatric hospital until he could be deemed competent to stand trial, agreed to the interview and told Baker that he remembered him from the standoff at the federal building.

Whatever broader lessons Irvin and Baker have drawn from the interviews, they have also used them as opportunities to establish bonds with people they may meet again in far less relaxed circumstances.

“When the relationships are formed, it makes it a little more difficult for them to think about not just putting themselves at risk but also the responders,” Irvin said.