Baldwin, 66, who is set to face trial in New Mexico in July on involuntary manslaughter charges, was also said to have had “no control of his emotions”.
Cinematographer Halyna Hutchins, 42, died on set in 2021 when a prop gun held by the Hollywood actor fired live ammunition.
Baldwin denies the charges and and his defence team has attempted to dismiss the case.
A court filing last month saw Baldwin’s lawyers accuse the prosecution of failing to provide evidence to a grand jury that would have helped his case.
But prosecutors have now responded, claiming that the “unconcerned” star had no control over his emotions, The Times reports.
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Kari Morrissey and Jason Lewis, said that Baldwin would scream on site, which contributed to safety issues throughout production.
Morrissey wrote: “To watch Mr Baldwin’s conduct on the set of Rust is to witness a man who has absolutely no control of his own emotions and absolutely no concern for how his conduct affects those around him.”
Rust director, Joel Souza, was also hurt during the event on the set in October 2021 when Hutchins died.
Baldwin claims he did not pull the trigger, merely the gun’s hammer, but prosecutors claim an analysis of the weapon reveals that the trigger was pulled.
Morrissey and Lewis stated in their most recent filing that Baldwin’s account of events had changed several times.
“Every time Mr Baldwin spoke, a different version of events emerged from his mouth, and his later statements contradicted his previous statements,” the pair said.
Timeline of events surrounding the fatal shooting
HALYNA Hutchins was killed on the set of Western blockbuster ‘Rust’ – here is a timeline of key events that followed the tragedy.
October 21, 2021 – Cinematographer Halyna Hutchins is shot and killed by a prop gun that actor Alec Baldwin was rehearsing with
Nov 17, 2021 – The script supervisor files a lawsuit accusing Baldwin of ‘playing Russian roulette’ by pointing revolver at Hutchins
Dec 2, 2021 – Baldwin speaks out and denies pulling the trigger and said he has ‘no idea’ why live rounds where on set
Jan 12, 2022 – Armourer Hannah Gutierrez-Reed files a lawsuit against the ammunition box manufacturer for ‘failing to state the boxes contained both live and dummy rounds’
Feb 15, 2922 – Hutchins’ family files wrongful death suit against Rust’s producers
April 20, 2022 – Rust production fined over failures that led to ‘avoidable death’
October 5, 2022 – Hutchins’ family reach settlement with production company and Baldwin
Nov 11, 2022 – Baldwin files lawsuit alleging negligence of several crew members
Jan 31, 2023 – Involuntary manslaughter charges announced against Baldwin and Gutierrez-Reed
Feb 23, 2023 – Baldwin pleads not guilty
March 31, 2023 – David Hall, Rust’s first assistant director, sentenced to six months probation after pleaded guilty for unsafe handling of a firearm
April 20, 2023 – Manslaughter charges against Baldwin dropped
June 22, 2023 – Gutierrez-Reed additionally charged with tampering with evidence
August 9, 2023 – The armourer pleads not guilty
Jan 19, 2024 – Baldwin indicted by grand jury again for manslaughter
Jan 31, 2024 – Baldwin again pleads not guilty
July 2024 – Baldwin will face trial
They added that Baldwin’s claim that he did not pull the trigger was “absurd on its face”.
Morrissey and Lewis were assigned to the case last March when the initial prosecutor stepped down.
A month later, the charges against Baldwin were dismissed.
But in January, authorities charged him with involuntary manslaughter after concluding that he pulled the trigger.
Morrissey stated in the latest filing that after being appointed to the case, she consented to meet with the actor’s lawyers, who delivered a PowerPoint presentation stating that the claims were unfounded.
They are reported to have stated that they will depend on evidence from stars like Harrison Ford and Dame Helen Mirren on Baldwin’s behalf.
The prosecution claim that several of the defence team’s points during the April meeting were “false or misleading”.
It comes after a Rust crew member has already been found guilty of involuntary manslaughter over Hutchins’s death.
Armourer conviced
Film armourer Hannah Gutierrez Reed was found guilty in the death of a cinematographer on set and dragged to jail to begin her sentence.
Reed was convicted of involuntary manslaughter and faces up to 18 months in jail after Halyna Hutchins was shot dead in 2021 when actor Alec Baldwin fired a prop gun with live ammunition.
The mum-of-one, 42, was shot when Baldwin fired the prop gun during rehearsal from point blank range and later died in hospital.
Reed, 26, had mistakenly loaded a live round into an imitation Colt .45 revolver, which was handed to Baldwin who could also face time behind bars.
A court jury concluded that she had negligently allowed the live ammunition on set on Wednesday after just two hours of final deliberation.
She was led away by cops to begin her sentence immediately and wore a blank expression as her mum cried nearby in the courtroom.
Hutchin’s family later said they “look forward” to others responsible for her death facing their day in court – a possible reference to Baldwin.
The Mission Impossible star could now face the same sentence as Reed, who pleaded guilty before her conviction.