Prosecutors are asking for a swab of DNA from Rex Heuermann -- the prominent New York City architect turned suspect in the Gilgo Beach murders.

Heuermann is charged with three counts of first-degree murder for the killings of Melissa Barthelemy in 2009 and Megan Waterman and Amber Costello in 2010, according to the Suffolk County district attorney's office.

He is also the prime suspect in the 2007 disappearance and death of a fourth woman, Maureen Brainard-Barnes, according to a court document from prosecutors.

Heuermann has not been charged in connection with that fourth homicide, but the investigation "is expected to be resolved soon," the document says.

Through his attorney, Heuermann has refuted the charges against him.

"I did not do this," Heuermann said after his arrest, according to his court-appointed attorney, Michael Brown.

The DA's office has submitted a court request to obtain a swab of DNA from Heuermann, a spokesperson from the office said Thursday. CNN is working to obtain a copy of the document requesting a DNA sample.

For years, the Gilgo Beach murders terrorized New York residents and sparked conflicting theories about whether a serial killer was responsible. The case grew cold for more than a decade.

A key break in the case came this year, when investigators recovered Heuermann's DNA from pizza crust that was thrown away in a Manhattan trash can in January.

Earlier Thursday, an attorney for Heuermann's wife told CNN that neither he nor his client have been contacted by investigators or asked by the district attorney to give DNA samples.

But authorities already have DNA samples from the suspect's wife, Asa Ellerup. They were collected from bottles inside a trash can outside the couple's shared home -- and linked through mitochondrial DNA testing to hairs found on or near three of the slain victims.

Evidence shows Heuermann's wife and children were out of the state when the three women are believed to have been killed, Suffolk County District Attorney Ray Tierney said last month.

"So with regard to that DNA and those hairs, it's either transfer -- in other words, one person comes into contact with a second person who then comes into contact with a third person -- or, they were at a location where you know the family member occupied, whether it's a car or a house," Tierney said.

Investigators believe the killings might have happened in the suspect's home in Massapequa Park, New York.

A source involved in the investigation told CNN the fact that the victims disappeared during times when the suspect's family was out of town suggests he may have lured victims to the Long Island home.