Over the course of 33 years, Robert A. Durst, the wealthy, peripatetic son of a New York real estate family, has been an elusive suspect in the deaths of three people in three states.

He was found not guilty of murder in a 2001 killing in Texas despite gruesome testimony that he cut up the body of a neighbor and tossed the pieces into Galveston Bay. Investigators in New York and Los Angeles have long been frustrated by their inability to bring charges against him relating to the 1982 disappearance of his first wife, Kathleen Durst, and the execution-style killing of a close friend and confidante.

But the district attorney in Los Angeles has recently reopened an investigation into the killing of Mr. Durst’s friend, Susan Berman, in December 2000, and is tying it to the case about his missing wife in New York, according to four people who have spoken to investigators.

Their inquiry could be bolstered by new evidence shown publicly for the first time on Sunday in the fifth episode of an HBO documentary about Mr. Durst: “The Jinx: The Life and Deaths of Robert Durst.” The evidence suggests that on the day Ms. Berman is believed to have been killed, Mr. Durst knew about her death and knew that her body was inside her Benedict Canyon home.