Alec Baldwin Shooting on 'Rust,' Fatal Shot Struck Cinematographer in Chest

Alec Baldwin was practicing a "cross draw" -- pointing his gun at the camera -- when a live round struck the director in the shoulder and the cinematographer fatally in the chest ... this according to new court documents.

Director Joel Souza told Sheriff's investigators he heard someone -- we're told the assistant director -- say "cold gun" while they got ready for the scene ... meaning the gun did not have live rounds in the chambers. Significantly, it appears the gun had been inspected before the lunch break but Souza could not remember if it had been checked when the crew returned.

A cameraman named Reid Russel told authorities, "Alec was trying to explain how he was going to draw out the firearm and where his arm would be when the firearm was pulled from the holster."

Souza explained Baldwin pointed the gun directly at the camera and fired, striking him in the shoulder and Halyna Hutchins in the chest. Souza says he had a vague memory that Hutchins was complaining about her stomach and grabbing her midsection. He says she then began to stumble backward and was assisted to the ground. He says he was bleeding from his shoulder and could see blood on Halyna.

Russel said after the shooting, Halyna said she could not feel her legs. Once on the ground, medics frantically began treating her as she was bleeding on the ground. She was airlifted to a hospital, where she was pronounced dead.

Steve Wolf, a special effects coordinator and theatrical firearms safety expert, told CNN there were 3 errors committed that resulted in the tragedy -- using a real gun rather than a prop gun, having a live round in the gun and having people stand behind the camera in the "line of fire." He also said the assistant director should not have been the one to clear the gun before the incident  ... that should have been the armorist's job.

Souza told authorities ... there should never have been live rounds near or around the scene that's being rehearsed or shot.

Authorities have obtained a search warrant to seize all camera footage and any other computer data that may have recorded the fatal incident.