Police Reveal How Rex Heuermann Reacted to Being Arrested in Gilgo Beach Murders Case

Rex Heuermann, the man police allege is the Long Island Serial Killer, was "very quiet" when police arrested him last Thursday on allegations he murdered three women more than a decade ago.

Suffolk County Police Commissioner Rodney K. Harrison tells PEOPLE Heuermann, 59, "kept to himself" and made "no statements" when he was taken into custody in Midtown Manhattan.

"I believe once one of our officers said he had him under arrest, he said, 'Why?' But that's pretty much the most I'm being told what he said," Harrison says.

Police read Heuermann his Miranda rights and Heuermann "said he [wanted] a lawyer," Harrison says.

"And he's still been quiet since he's been over at Riverhead [Correctional Facility]," Harrison adds.

Meanwhile, authorities are reportedly searching Heuermann's house in search of forensic evidence related to the allegations.

Heuermann, a Manhattan architect and a married father of two, was charged with three counts of first-degree murder and three counts of second-degree murder in the deaths of Amber Costello, 27, Melissa Barthelemy, 24, and 22-year-old Megan Waterman. He has pleaded not guilty.

He is also considered a prime suspect in the death of 25-year-old Maureen Brainard-Barnes.

The four women’s remains were discovered along a half-mile stretch at Gilgo Beach on Long Island, N.Y., in December 2010. All four women had worked as online escorts and were reported missing between 2007 and 2010.

At least 10 bodies were discovered at the beach, but investigators have said not all of them are believed to be connected to the same killer.

The case remained unsolved for more than a decade and gained notoriety after the investigation became the focus of author Robert Kolker’s 2013 bestselling nonfiction book Lost Girls, and later a true crime Netflix movie of the same name.

The killer allegedly used four separate burner phones to contact the women and “lure them out to Massapequa,” Suffolk County District Attorney Ray Tierney told PEOPLE last week. “Then he would murder them, and then he would discontinue the use of the burner phone. He did that four times.”

Family members of some of the victims also reported they received taunting phone calls from a man who claimed to be the killer. 

Tierney said after Heuermann’s arrest that investigators found a “concerning” internet search history that allegedly showed the Massapequa man had “obsessively” looked up his victims and their siblings. 

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Other online activity allegedly showed Heuermann had looked up information about the Gilgo investigation “over 200 times” in a 14-month span and searched specific terms, such as “why could law enforcement not trace the calls made by the long island serial killer” and “why hasn’t the long island serial killer been caught,” according to the district attorney.

Investigators first zeroed in on Heuermann after a witness gave a description of a vehicle believed to be used by the killer. Detectives then used motor vehicle records to track down Heuermann and his Chevy Avalanche, which helped lead to his address and later his DNA.

Harrison, the police commissioner, says Heuermann’s family was in "shock" and "disbelief" when they learned of his alleged double life. 

"We had to kind of show them some type of proof to let it be known who their father was behind the curtain," Harrison says. "But they're cooperating."