Alec Baldwin was not asked to remain in New Mexico while the investigation into the "Rust" movie shooting takes place, Fox News can confirm.

The Santa Fe County Sheriff’s public information officer, Juan Rios, told Fox News, "No one's been charged or arrested. So you don't impose those types of things on people."

"And we're always of the mindset that people will be, if they don't live here, that they will continue to be cooperative with the investigators," he added.

On Thursday, Baldwin accidentally shot two people, killing "Rust" cinematography Halyna Hutchins, and injuring "Rust" director Joel Souza when he discharged a gun after being told it was "cold" or unloaded, per affidavits. 

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The Western movie was filming at Bonanza Creek Ranch near Santa Fe, New Mexico and currently, the Santa Fe Sheriff’s Department is investigating the incident. 

Baldwin has since spoken out about the incident, calling it a 'tragic accident' and praising Hutchins as a 'deeply admired colleague.' (Jim Weber/Santa Fe New Mexican)

The production company also confirmed it will be "conducting an internal review of our procedures while production is shut down" and providing mental health services to the cast and crew in light of the tragedy. 

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"The safety of our cast and crew is the top priority of Rust Productions and everyone associated with the company. Though we were not made aware of any official complaints concerning weapon or prop safety on set, we will be conducting an internal review of our procedures while production is shut down. We will continue to cooperate with the Santa Fe authorities in their investigation and offer mental health services to the cast and crew during this tragic time," the producers said in a statement obtained by Fox News. 

Cinematographer Halyna Hutchins was killed on the New Mexico set of 'Rust' when a projectile was accidentally fired from a gun. (AP/Getty Images)

Baldwin made a statement on social media Friday about Hutchins' death. He expressed his condolences to Hutchins' family and called the shooting an accident.

"There are no words to convey my shock and sadness regarding the tragic accident that took the life of Halyna Hutchins, a wife, mother and deeply admired colleague of ours," he said Friday morning on Twitter.

"I'm fully cooperating with the police investigation to address how this tragedy occurred and I am in touch with her husband, offering my support to him and his family. My heart is broken for her husband, their son, and all who knew and loved Halyna," the actor concluded.  

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Hutchins' husband, Matthew, told Fox News on Friday, one day after his wife's death, that he had made contact with Baldwin.

This aerial photo shows the Bonanza Creek Ranch in Santa Fe, N.M., Saturday, Oct. 23, 2021. (AP Photo/Jae C. Hong)

"I have spoken with Alec Baldwin, and he is being very supportive," Matthew Hutchins told Fox News. 

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Baldwin was spotted Matthew and his 9-year-old son in Santa Fe. The two had an emotional meeting in which they were photographed hugging each other.