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MIDDLEBURY, Vt. — It was December 1971, and Lynne Schulze was in her dorm room, looking for her favorite pen before a final exam. But the Middlebury College freshman never showed up for the 1 p.m. test.

At 2:15 p.m., she was spotted across the street from a local health food store, one she had visited earlier in the day. She was never seen again.

More than four decades later, police in this small college town are focusing their investigation into Schulze’s disappearance on the man who owned that modest store: multimillionaire murder suspect Robert Durst.

A day after the stunning revelation that the eccentric, notorious figure had been a subject of the Vermont cold-case investigation since 2012, Middlebury police Tuesday provided new details about Durst’s apparent proximity to the 18-year-old on the day she vanished. Durst’s alleged involvement in other “nefarious activities,” authorities in town said, only deepened their suspicions.

“This is a person who is very interesting to us,” said Thomas Hanley, the Middlebury police chief. “We certainly would like to talk to him.”

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Police in Middlebury are the latest authorities to focus attention on Durst, the troubled heir to a New York real estate empire who was arrested this month and charged with the 2000 killing of Susan Berman, a longtime friend.

In a bizarre twist, Durst was arrested in New Orleans the day before the final episode of an HBO series on his life aired, bringing new attention to his alleged connections with the Berman case and two others: the 2001 death of a 71-year-old neighbor and the 1982 disappearance of his wife. During the show, Durst was recorded off camera saying, “What the hell did I do? Killed them all, of course.”

Following Durst’s arrest, FBI officials have advised local investigators in areas where Durst, 71, has lived to reexamine cold cases for possible connections, a spokesman said. But in Vermont, police had been eyeing Durst since 2012, when they received a tip that he had owned a health food shop in town at the time of Schulze’s disappearance. After years of false leads, it was a promising development, authorities said Tuesday.

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Durst’s store was named “All Good Things,” which became the title of a 2010 movie based on Durst’s story.

Middlebury police did not describe him as a suspect and said they have no evidence that Durst and Schulze “had any personal contact” but they are investigating a potential connection.

“We know Lynne stopped at the store the last day she was seen,” Detective Kris Bowdish said at an afternoon news conference where authorities gave a timeline of Schulze’s movements on the day she disappeared.

Around 12:30 p.m., Schulze was seen at the bus stop beside Durst’s store, eating prunes she had bought there, investigators said. Schulze told a student she was waiting for a bus to New York, but returned to campus when she learned it had already left.

Around 2:15, Schulze was again spotted near the store.

“This is the last time she is ever seen,” Bowdish said.

Police said they do not believe Durst was ever interviewed at the time. He lived in Middlebury less than two years, they said.

All of Schulze’s belongings, including her wallet and identification, were found in her dorm room.

Relatives of Schulze could not be reached for comment Tuesday. Police said the family had asked for privacy, but were “very interested in the lead” after so many years.

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“They would very much like some resolution and closure,” Bowdish said of Schulze’s siblings. Her parents have died.

Hanley, the police chief, said investigators reopened the case in 1992 and “began from square one.”

Several detectives have since headed up the investigation, but have never made substantial progress.

Despite the passage of time, authorities say they are hopeful someone will come forward with information about that day or a possible link between the two.

“We don’t let open cases like this, where someone has died, go away,” Hanley said.

Durst has long denied any involvement in Berman’s shooting or his wife’s disappearance. In 2003, he admitted to killing his neighbor, but was acquitted after pleading self-defense.

He is being held without bail as a potential flight risk. He has been held in a mental health unit, and is considered a suicide risk.

His lawyer, who could not be reached for comment Tuesday, has maintained his client is innocent.

Friends of Schulze, who grew up in Simsbury, Conn., said that although details remain scarce, they remain optimistic her disappearance will be solved.

“We are hoping and praying for resolution about what happened to our dear one 44 years ago,” said Susan Randall, a high school friend.

Coming at the end of the semester, Schulze’s disappearance was not reported for several days, and her parents asked police to keep it private until late January as they awaited her return.

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There were many reported sightings of Schulze, police said, but none were found credible.

In Middlebury, many people found the sudden spotlight on the town unsettling as they revisited the young woman’s sudden disappearance.

“Nobody knew anything. Even in the papers, nobody knew,” said Reg Spooner, 77, who grew up in Middlebury.

In those days, Spooner said, Middlebury was much smaller. A disappearance — and an apparent murder — was unheard of.

Jerry Huestis, 50, who lives at the site of the former health food store, said Durst’s potential connection gave him an “eerie feeling.’’

“It’s bad enough seeing what the guy looked like, but knowing he was here?”

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Steve Annear and Jeremiah Manion of the Globe staff contributed to this report.