LOS ANGELES—Having been named by the “Rust” film’s chief lighting technician as a co-defendant in a lawsuit stemming from the on-set 2021 fatal shooting of cinematographer Halyna Hutchins, the movie’s assistant director has filed a cross-complaint against Alec Baldwin and other crew members.

Ms. Hutchins, 42, was killed by a bullet fired by Baldwin, 65, from a prop weapon on the New Mexico set. Plaintiff Serge Svetnoy maintains the Oct. 21, 2021, shooting “was caused by the negligent acts and omissions” of actor/producer Mr. Baldwin, assistant director David Halls, and other crew members.

In his Los Angeles Superior Court suit filed in November 2021, Mr. Svetnoy also states that gunpowder and other residual materials struck the right side of his face.

Mr. Halls’ cross-complaint, brought Friday, names as defendants Mr. Baldwin, armorer Hannah Gutierrez-Reed, prop supplier Seth Kenney, and prop master Sarah Zachry.

Assistant director Mr. Halls, while denying any wrongdoing in Mr. Svetnoy’s suit, seeks indemnity from those individuals in the event he is held liable.

In March, Mr. Halls was sentenced to six months unsupervised probation as part of a plea deal in connection with the set shooting.

Mr. Svetnoy was among the first “Rust” crew members to publicly speak out about the shooting of Ms. Hutchins while Mr. Baldwin was helping to prepare camera angles on the film’s set near Santa Fe. The weapon, which was supposed to contain only blank rounds, discharged a lead bullet that struck Ms. Hutchins in the chest and lodged in the shoulder of director Joel Souza, now 50.

Mr. Svetnoy wrote on social media days later that he witnessed the shooting and comforted the bleeding Ms. Hutchins until paramedics arrived. He immediately deemed the shooting an act of negligence, saying armorer Hannah Gutierrez-Reed and Mr. Halls both failed to check the weapon before declaring it safe and passing it to Mr. Baldwin.

Ms. Gutierrez-Reed, 26, has pleaded not guilty in New Mexico to charges of involuntary manslaughter and evidence tampering in Ms. Hutchins’ death.

Serge Svetnoy, chief lighting technician for the film "Rust," speaks alongside his attorney about a lawsuit filed after the fatal shooting on the film during a press conference in Los Angeles on Nov. 10, 2021. (Patrick T. Fallon/AFP via Getty Images)