Alec's blood-stained costume from the movie has been taken as evidence, as well as the gun that went off, plus other prop guns and ammo being used on set, according to the warrant.
The warrant says Halyna Hutchins was shot in the chest and Joel Souza was wounded as he was standing behind her.
A source working on the movie tells us gun safety has been a consistent issue on set, and just last weekend blank rounds were shot when they weren't supposed to go off.
As we reported ... Alec pulled the trigger on the gun and the accident resulted in the death of 42-year-old cinematographer Hutchins. She was struck and airlifted to a hospital, where she died. Director Souza was also hit, but has reportedly been released from the hospital.
Baldwin says he's cooperating with the investigation and says, "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."