Hutchins died after being hit in the stomach while Souza was struck in the shoulder and hospitalised as a result of his injuries, with the director revealing she stumbled backwards after a "whip and a loud pop" of a gun, according to an affidavit obtained by the Los Angeles Times.
It reads, "Joel stated that they had Alec sitting in a pew in a church building setting, and he was practicing a cross draw. Joel said he was looking over the shoulder of (Hutchins), when he heard what sounded like a whip and then loud pop."
"Joel then vaguely remembers (Hutchins) complaining about her stomach and grabbing her midsection. Joel also said (Hutchins) began to stumble backwards and she was assisted to the ground."
According to the papers, Baldwin, who was handed the gun and told it was "cold" by assistant director David Halls, was "hysterical and absolutely inconsolable for hours" after accidentally shooting his colleague.
Halls had reportedly previously been the subject of complaints about his behaviour and safety on set, while the affidavits which also cite cameraman Reid Russell, who told investigators Baldwin was always careful with weapons on set.
The incident came amid turmoil on set, with several members of the camera crew walking off the production in a dispute over payment and lodging.
"Reid stated that the camera crew was having issues with production involving payment and housing," it reads, adding that six individuals had walked out.
Meanwhile, Serge Svetnoy, chief electrician for "Rust", blamed "negligence and unprofessionalism" for Hutchins' death in a post on Facebook, in which he revealed he held her in his arms following the incident.
Following the incident, Baldwin took to Twitter to express his condolences to the director of photography's loved ones, after the tragic accident on the Santa Fe, New Mexico set.
"There are no words to convey my shock and sadness regarding the tragic accident that took the life of Halyna Hutchins, a wife, mother and deeply admired colleague of ours," he wrote.
"I'm fully cooperating with the police investigation to address how this tragedy occurred and I am in touch with her husband, offering my support to him and his family. My heart is broken for her husband, their son, and all who knew and loved Halyna."