Her father, Thell Reed, a well-known Hollywood armourer, would not comment, but said that he "wasn't there" and had nothing further to add.
Hutchins was shot and killed with a gun discharged by Alec Baldwin, who had been told the firearm was unloaded, during a rehearsal for the film.
The director Joel Souza was also wounded but is expected to fully recover.
It was just Gutierrez Reed's second film as lead armourer. She was one of three people who handled the gun before it was fired by Baldwin.
Santa Fe County sheriff Adan Mendoza said the investigation is focusing on how a live round made its way into the weapon and on to the film set.
Meanwhile, the armourer's lawyers have claimed the bullets she loaded into the gun on the day of the shooting were taken from a box that supposedly contained only dummy rounds incapable of firing.
The ammunition was left unattended from around 11am to 1pm that day, meaning there was an opportunity for someone to have mixed a live round into the box.
Lawyer Jason Bowles said they were "assuming" the live round came from that box.
"We're assuming somebody put that live round in that box, which, if you think about that, the person who put the live round in the box of dummy rounds had to have the purpose of sabotaging the set. There's no other reason you would do that. That you would mix that live round with the dummy rounds."
The idea of intentional sabotage is just one of the many theories they are investigating, he said.
Gutierrez Reed previously dismissed speculation that the accidental shooting was her fault, saying she asked for safety meetings on the film but was rebuffed.
She blamed rushed conditions and low budget on set for the casualty.
Her lawyers said safety on set was her "number one priority".
"Ultimately, this set would never have been compromised if live ammo were not introduced. Hannah has no idea where the live rounds came from."
