Alec Baldwin has yet another lawsuit to deal with regarding the fatal "Rust" shooting ... family members of the late Halyna Hutchins are taking the actor and several others to court.
According to legal docs, obtained by TMZ, Halyna's parents and sister have named Alec -- as well as a slew of companies and individuals -- as defendants in the suit. Armorer Hannah Gutierrez-Reed is one of the many named.
The docs claim several safety protocols on set were ignored, including their insistence that Gutierrez-Reed should've been the only one handing Baldwin the gun -- NOT Assistant Director David Halls, who's also named as a defendant.
The family says Baldwin "cannot hide" behind Halls' alleged statement on set that the gun was "cold" ... adding a veteran actor like himself should've insisted that it was demonstrated to him or checked it himself.
What's more, the docs say the scene they were filming didn't call for Baldwin's gun to be cocked or fired at all -- and they say there was insufficient plexiglass in the building at the time of the incident, which could've ensured Hutchins' safety.
Hutchins' family is suing for loss of consortium, negligence, intentional infliction of emotional distress, and more ... and is seeking unspecified damages.
We've reached out to Baldwin and Gutierrez-Reed -- Hannah's lawyer, Jason Bowles, had no comment ... no word from Baldwin's team.
As we reported, Baldwin was charged with involuntary manslaughter last week ... with the D.A. listing many of the same reasons as to why he was hit with the charge -- also pointing out potential discrepancies in his multiple interviews following the shooting.