The family of a cinematographer shot and killed on the set of the film Rust is suing Alec Baldwin and the movie’s producers for wrongful death, their lawyers say.

Lawyers for the family of Halyna Hutchins announced the lawsuit filed in New Mexico in the name of Ms Hutchins’ husband, Matthew, and their son, Andros, at a Los Angeles news conference on Wednesday morning (Australian time).

At least three other lawsuits have been filed over the shooting, but this is the first directly tied to one of the two people shot.

The “reckless conduct and cost-cutting measures” of Baldwin and the film’s producers “led to the death of Halyna Hutchins”, lawyer Brian Panish said.

A video created by the lawyers showed an animated recreation of the shooting.

It showed Baldwin pointing a gun at Ms Hutchins during the set-up for the filming of a scene for the western in New Mexico on October 21 when it went off, killing Ms Hutchins and wounding director Joel Souza.

Baldwin has said he was pointing the gun at Ms Hutchins at her instruction and it went off without him pulling the trigger.

The attorneys said in the video that Baldwin had turned down training for the kind of gun draw he was using when he shot Ms Hutchins.

It said industry standards required a rubber or similar prop gun to be used during the set-up, and there was no need for a real gun.

Last month, nearly three months after the shooting, Baldwin turned over his mobile phone to authorities in his home state of New York. They gathered information from it and gave it to Santa Fe County investigators, who had a warrant for it.

Investigators have described “some complacency” in how weapons were handled on the Rust set. They have said it is too soon to determine whether charges will be filed.

Halyna Hutchins was killed after being shot in the chest with a live round.

Baldwin said he did not believe he would be criminally charged in the shooting.

The film’s script supervisor and its lead camera operator, both of whom were standing nearby when Ms Hutchins was shot, have each filed a lawsuit alleging trauma.

And the film’s armourer Hannah Gutierrez Reed, who was named as a defendant in those lawsuits and blamed by some for the shooting, has filed her own suit saying an ammunition supplier created dangerous conditions by including live ammunition in a box that was supposed to hold only dummy rounds.

In an interview with the US’s ABC News in December, Baldwin said he felt incredible sadness about the shooting, but no guilt.

“Someone is responsible for what happened, and I can’t say who that is, but it’s not me,” Baldwin said.

He said Ms Hutchins had asked him to point the gun just off camera and toward her armpit before it went off.

“I didn’t pull the trigger,” Baldwin said. “I would never point a gun at anyone and pull the trigger at them. Never.”