Alec Baldwin Hasn't Turned Over Cell Phone Nearly 1 Month After Search Warrant Issued, Detectives Say

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Alec Baldwin has yet to turn over his cell phone to authorities, despite publicly claiming to be cooperating with the Rust investigation and the related search warrants.

The Santa Fe County Sheriff's Office said in a press release Thursday that they applied for a search warrant asking for the actor's phone on Dec. 16, and the request was approved by a judge that same day. Detectives then served the warrant to Baldwin's lawyers via email, who they say acknowledged they got the message.

The sheriff's office then got the Santa Fe District Attorney's Office involved when Baldwin "had not immediately provided his phone pursuant to the initial search warrant," per the release. The DA's office then took over the efforts to retrieve the phone "on a consent basis" because of "jurisdictional concerns," they stated.

According to the press release, investigators were told on Dec. 20 that negotiations were underway to get the cell phone and its contents, however, as of Thursday, "the cell phone has not been turned over to authorities."

Aaron Dyer, Baldwin's civil attorney at the Pillsbury, Winthrop, Shaw, Pittman, responded in a statement to PEOPLE: "We reached an agreement last weekend with the Santa Fe Sheriff's Office and the Santa Fe District Attorney's Office, and Mr. Baldwin's phone is being turned over this week for review. Ever since this tragic incident, Mr. Baldwin has continued to cooperate with the authorities, and any suggestion to the contrary is simply untrue. We requested that the authorities obtain a warrant so that we could protect his privacy on other matters unrelated to Rust and have been working through that process. We are finalizing logistics with the authorities in New York who are assisting in this matter."

Baldwin, 63, said on Saturday that the process to fulfill the search warrant for his phone is complicated, maintaining that he is fully cooperating with the investigation. "Any suggestion that I am not complying with requests or orders or demands or search warrants about my phone, that's bull----, that's a lie," he said in a video on Instagram.

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Noting that authorities from another state have to go through the state in which he lives in order to make a request for his phone, Baldwin continued, "They have to specify what exactly they want. They can't just go through your phone and take, you know, your photos or your love letters to your wife or what have you."

"But of course, we are 1000 percent going to comply with all that. We are perfectly fine with that," he added. "The best way, the only way, we can honor the death of Halyna Hutchins is to find out the truth. That's what I'm working toward, insisting on, demanding."

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Hutchins is the 42-year-old cinematographer who was fatally shot on the New Mexico set of Rust. Baldwin was holding the gun that discharged, shooting her and director Joel Souza, who was injured.

Back in December, Baldwin gave an emotional first interview since the tragedy, telling ABC News' George Stephanopoulos that he thinks it's "unlikely" he'll personally face criminal charges, adding that he continues to cooperate in investigations.

"I don't have anything to hide," he said at the time.

Added Baldwin, "I want to make sure that I don't come across like I'm the victim, because we have two victims here. All of what happened that day leading up to this event was precipitated on one idea, and that idea is that Halyna and I had something profound in common. That is we both assumed the gun was empty, other than those dummy rounds."