The unnamed director did not know the prop contained live ammunition and indicated it was unloaded by shouting "cold gun!", the records say.
Cinematographer Halyna Hutchins was fatally shot in the chest in Thursday's incident on the set of the film Rust.
Director Joel Souza, who was standing behind her, was wounded.
The 48-year-old received emergency treatment for a shoulder injury and was later released from hospital.
Further details of the police investigation were released on Friday when a search warrant was filed at a court in Santa Fe, New Mexico.