Numerous others are also named in the suit, including armourer Hannah Gutierrez-Reed and assistant director David Halls, Fox News reports. Production companies and producers are also named in the suit which accuses the individuals of neglecting to ensure firearm safety guidelines were followed.
The family of Hutchins is seeking punitive damages plus funeral and burial expenses.
Baldwin's lawyer Aaron Dyer denied any wrongdoing from the actor.
"Everyone's hearts and thoughts remain with Halyna's family as they continue to process this unspeakable tragedy. We continue to cooperate with the authorities to determine how live ammunition arrived on the Rust set in the first place. Any claim that Alec was reckless is entirely false," he told Fox News.
"He, Halyna and the rest of the crew relied on the statement by the two professionals responsible for checking the gun that it was a 'cold gun' — meaning there is no possibility of a discharge, blank or otherwise," he said.
"This protocol has worked on thousands of films, with millions of discharges, as there has never before been an incident on a set where an actual bullet harmed anyone. Actors should be able to rely on armourers and prop department professionals, as well as assistant directors, rather than deciding on their own when a gun is safe to use."