Alec Baldwin attended a poker night at New York City private club Zero Bond hours after criminal charges were filed against him, a source tells PEOPLE.

The source says that "Alec seemed chill and low-key" as he visited the exclusive spot in the NoHo neighborhood of Manhattan with his wife, Hilaria Baldwin, adding: "They didn't engage with anyone but headed straight to where everyone plays poker."

The area at the back of the private members' club is only available to poker players, the source tells PEOPLE.

"After spending around 30 to 40 minutes in the back poker area, Alec and Hilaria came back out and sat in the lounge," the source says, adding that the pair "chatted away" in the lounge. (Fox News obtained photos of Alec outside of Zero Bond on Wednesday.)

Zero Bond states on their website that they maintain a "rigorous process in regards to member selection," and only members who "display a high level of integrity" and demonstrate an ability to contribute to the private community are accepted.

Once a potential member submits a formal application and is accepted into the club, they are required to pay an initiation fee and an annual fee that varies by age.

Baldwin's visit to the exclusive club came after he and Rust armorer Hannah Gutierrez-Reed were formally charged for their involvement in the on-set death of Rust cinematographer Halyna Hutchins on Oct. 21, 2021.

The charges against Baldwin and Gutierrez-Reed, 25, include two counts of involuntary manslaughter. Hutchins' death came after a prop gun held by Baldwin — that contained live rounds — was discharged.

While Baldwin expressed during his first interview following the incident that he "didn't pull the trigger" on the gun — and his attorney Luke Nikas of Quinn Emanuel told PEOPLE in a statement that they will "fight these charges" — a judge will next decide whether to move the case forward after a preliminary hearing.

RELATED VIDEO: FBI Investigation Determines Alec Baldwin Must Have Pulled Trigger in 'Rust' Shooting: Report

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Tuesday's charge against the actor and armorer by Santa Fe County District Attorney Mary Carmack-Altwies comes after she announced she'd file charges before the end of the month "in keeping with her commitment to pursue justice for all victims and to hold everyone accountable under the law," via a statement issued Jan. 19.