THIS is the shocking moment a hostage was accidentally killed by LA cops as they tried to free her in the first death of its kind in 13 years.

Guillermo Perez was captured on police bodycam holding a knife to Elizabeth Tollison’s throat as officers surround the pair outside a church.

When the 32-year-old attacker ignored commands to drop the blade and started to slice her neck the cops opened fire.

They let off 18 rounds killing both the assailant and, tragically, his victim.

It is the first time in 13 years the LAPD killed someone they consider an “innocent bystander or hostage”.

Now Tollison’s family have filed a claim against the police department and the city, lawyers announced yesterday.

They said at a news conference that officers showed no regard for her life as she was briefly held hostage.

Both Perez and Tollison were homeless.

But Brian Dunn, the attorney representing Tollison's family, said that a doctor told Tollison's son that she only had a cut on her cheek and that it was not life-threatening.

On June 16, police arrived at the church after a 911 call reported a man had stabbed his ex-girlfriend.

Witnesses told police that Perez moved the knife in a "sawing motion against her throat and cut her throat," Cmdr. Alan Hamilton, who leads the unit that investigates police shootings, said in the video.

Tollison's son, Jesse Pelaez, said at Wednesday's news conference that he thinks that "if the hostage was somebody important, the situation would have been handled differently."

"It hurts me so much knowing I'll never be able to see, talk or listen to my mother again because the police didn't know how to handle the situation properly," he said.

Police Chief Michel Moore said Tuesday that "officers were forced to make split-second decisions based on the actions of a violent individual."

But Dunn said the department violated training protocols for handling suspects armed with weapons other than firearms and should have tried harder to de-escalate the situation.

"It is illogical and inconceivable for an officer on the scene to not realize that she will certainly be shot if 18 rounds are fired," Dunn said.

"They say this is a fast-moving situation," he said. "This is a fast-moving situation because they turned it into a fast-moving situation."

Department spokesman Josh Rubenstein did not immediately return a message Wednesday asking about the discrepancy over where Tollison was cut or about whether the department violated training protocols.

If the city rejects the claim for damages, the family can proceed to court with a lawsuit.