Alec and Hilaria Baldwin have been attempting to avoid attention while staying in Vermont as the investigation into the fatal shooting of "Rust" cinematographer Halyna Hutchins continues in New Mexico.

Despite the tragedy, both the actor and his wife are continuing to post on social media. Most recently, Hilaria posted about her lost cat (which was later found) and her kids' Halloween costumes while Alec tweeted political jabs at Sen. Joe Manchin, D. W.Va. 

PR and crisis management expert Andrew Gilman, who is the President & CEO CommCore Consulting Group, weighed in on how the Baldwins' Twitter and Instagram activity can be misinterpreted. 

"Hilaria may think it’s hilarious to post Halloween photos. She would be better off to wait another year to post photos of the Baldwin family having fun," Gilman told Fox News. 

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Meanwhile, "Alec Baldwin’s reputation goes up and down like a seesaw. The seriousness of even an inadvertent shooting is more challenging than the ill-spoken words and tantrums that have gotten him in trouble in the past."

"If I was advising him, after the initial statements of emotional support, care and concern, he should lay low for a while. He should continue with these sentiments until there is a finding from investigators that requires further comment," Gilman continued.

Alec Baldwin spoke to photographers alongside his wife, Hilaria Baldwin, roadside while in Vermont. 

Alec Baldwin spoke to photographers alongside his wife, Hilaria Baldwin, roadside while in Vermont.  (Fox News Digital)

On Saturday, the actor and producer conducted an impromptu press conference roadside in Vermont, during which he said he is cooperating with police and has been speaking to them every day regarding the fatal on-set shooting of cinematographer Halyna Hutchins. Baldwin maintained that he could not speak on the active investigation.

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"It's an active investigation in terms of a woman died. She was my friend," Baldwin said. "We were a very, very well-oiled crew shooting a film together, and then this horrible event happened."

Hilaria previously stepped out to grab food for the family in town.

Hilaria previously stepped out to grab food for the family in town. (Fox News Digital)

Baldwin discharged a gun on the set of "Rust" in New Mexico on Oct. 21, fatally shooting Hutchins and injuring director Joel Souza. Assistant director Dave Halls had told Baldwin that the gun was a "cold gun," meaning "not hot" or unloaded, after armorer Hannah Gutierrez Reed had placed the gun on a cart on set.

Prop master Sarah Zachary also handled the gun before the fatal shooting, according to a search warrant executed by the Santa Fe Sheriff's Office.

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The Santa Fe County Sheriff's Department is still investigating the incident and said it was "too early" to comment on potential charges during a press conference Wednesday. However, Sheriff Adan Mendoza has since referred to the department's efforts as a "criminal investigation."

Alec tweeted his initial statement the day (Oct. 22) after the on-set shooting. 

Alec tweeted his initial statement the day (Oct. 22) after the on-set shooting.  (Jim Weber/Santa Fe New Mexican  |  Twitter)

"I’d be careful using the word ‘accident,'" Mendoza said during an appearance Thursday on "Fox & Friends."

"This is obviously a tragedy, and it was avoidable, so right now it’s a criminal investigation."

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Baldwin made his initial statement about Hutchins' death the Friday after the on-set shooting. He tweeted one day after the shooting to share his initial thoughts with the public. 

"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 wrote at the time.

"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," Baldwin concluded.

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Hilaria wrote last week on Instagram, "MY HEART IS WITH HALYNA. HER HUSBAND. HER SON. THEIR FAMILY AND LOVED ONES. AND MY ALEC. IT’S SAID, ‘THERE ARE NO WORDS’ BECAUSE IT’S IMPOSSIBLE TO EXPRESS THE SHOCK AND HEARTACHE OF SUCH A TRAGIC ACCIDENT. HEARTBREAK. LOSS. SUPPORT," she penned in a text photo in all caps.