(CNN) The FBI is asking detectives across the country to dust off their cold case murder files and see whether millionaire heir Robert Durst could be connected to any other unsolved crimes.

Durst, the focus of HBO's true crime documentary series "The Jinx," was charged with first-degree murder last week in the 2000 killing of his longtime confidante, Susan Berman.

Now the FBI is putting out a call to local authorities to examine cold cases in locations near where Durst lived over the past five decades, a U.S. law enforcement official said. Unsolved cases in Vermont, upstate New York, the San Francisco Bay area and Southern California are among those getting a new look, the official said.

Durst's attorney, Dick DeGuerin, said it's a sign that authorities are desperate.

"They seem to be going to such great lengths to pin something else on him," DeGuerin said. "They must not have much of a case to begin with."

Durst, who authorities believe has a net worth of $100 million , has lived in numerous places and owned property in at least four states, according to court documents and public records.

In "The Jinx," Durst describes the time he spent living in Vermont with his first wife, Kathleen, running a health food store in the 1970s.

In 1982, Kathleen McCormack Durst went missing. Durst says he last saw her when he dropped her off at a train station in Katonah, New York, and she headed to their Manhattan apartment. Her family members say they believe she's dead and that Durst is the one to blame. The case has never been solved.

He's also lived in Galveston, Texas, where he admitted to shooting a neighbor and dismembering the body in 2001. He was acquitted in a 2003 murder trial after arguing he'd acted in self-defense.

She was shot dead in December 2000 in her Beverly Hills, California, home. Investigators know Durst was in California the week Berman died. It's a detail Durst shrugs off in the HBO documentary, in which he denied he had anything to do with Berman's death and said, "California's a big state."

Police: Durst is connected to missing Vermont college student

Authorities investigating a decades-old cold case in Vermont said Monday that there's a connection between Durst and the case of Lynne Schulze, a college student who disappeared from Middlebury College in 1971.

Lynne Schulze went missing when she was a student at Middlebury College in 1971.

"We are aware of the connection between the disappearance of Lynne Schulze and Robert Durst," Middlebury Police Capt. Tom Hanley said. "We have been aware of this connection for several years and have been working with various outside agencies as we follow this lead."

Hanley elaborated Tuesday on the nature of the connection, saying Durst owned a health food store where Schulze shopped the day she disappeared. But there is no evidence the two had met, Hanley said.

DeGuerin's attorney brushed off the accusation Monday.

"You know, he may have been in Chicago when Jimmy Hoffa disappeared," he said. "He's an easy target."

The name of the health food store, "All Good Things," was also the title of a 2010 film starring Ryan Gosling and Kirsten Dunst that was a thinly veiled fictional take on the Durst case.

After seeing the film, Durst reached out to director Andrew Jarecki and said he wanted to be interviewed. The interviews with Durst became the basis for "The Jinx."

Ties to California teen's disappearance?

Durst says in the documentary that he had traveled during the week of Berman's death to Trinidad, California, a small coastal city in northern California.

"It was very rural, very pretty," he says.

And it was a place, Durst says, where he lived "off and on."

In Eureka, about 20 miles south, Durst has been part of another investigation.

Authorities there say they haven't ruled out the possibility he could be connected to the disappearance of Karen Mitchell, who went missing in November 1997 when she was 16 years old.

Karen Mitchell went missing in Eureka, California, in 1997, when she was 16 years old.

The police chief said investigators were interested in learning what Durst has to say about that case now that he's behind bars.

"We are certainly interested in any information that may or may not come out of interviews with Mr. Durst," Police Chief Andy Mills said. "If information comes to us that allows us to further our investigation, then we will certainly take the opportunity to do that."

According to local news reports at the time of Mitchell's disappearance, she was last seen leaning into a light blue car that she might have gotten into. A witness gave police a description of the man behind the wheel, which resulted in a sketch of a gray-haired man with glasses -- a drawing that journalist Matt Birkbeck says looks remarkably like Durst.

"He wears these wide-rim glasses. He was wearing those glasses back in the day and it's also in the composite," said Birkbeck, whose book, "A Deadly Secret," chronicles Durst's life and run-ins with the law.

"Durst apparently knew Karen Mitchell. Karen had volunteered at a homeless shelter in Eureka, which Durst had frequented, which he had a habit of doing in different cities," Birkbeck said.

He'd also gone to a shoe store that Mitchell's aunt ran at a mall in Eureka, Birkbeck said.

The former lead investigator on the case, Dave Parris, retired several years ago and could not be reached for comment.

In 2003, he told The Journal News that there were similarities between Durst and the composite sketch.

"He's a lead we're following," Parris told the newspaper, "and with all the information we've learned about him, I'm not fully comfortable that I can eliminate him from our investigation at this point."

Author: Durst's path is tough to follow

Investigators looking at other cases across the country have their work cut out for them, Birkbeck said.

"In 2002, when my book was first published, we reported that police found six addresses in the San Francisco Bay area alone. Some of them were properties, some of them were post offices, some of them were warehouse facilities. There were other address in Northern California, Southern California, as well as other parts of the country," he told CNN's "Erin Burnett: Outfront."

But the investigation is nothing new, he said.

"They've been looking at this for several years now," he said. "I guess with recent events, they've really expanded their scope."