SOMETIMES, no lock on the door is secure enough.

As word spread in 2001 that alleged cuckoo killer Robert Durst had jumped bail, running from a murder charge, his youngest brother went into a panic, fearing he might be killed.

Thomas Durst is a real-estate developer in the tony Marin County, Calif., town of Ross. In late 2001, he walked into his local police station to seek protection from his gun-loving, wig-wearing, fugitive brother, should Robert decide to pay him a visit, two California law-enforcement sources close to the case told me.

“He said, ‘My brother’s on the run, I’m afraid for my life,’ – or words to that effect,” one source said.

Thomas begged the cops to assign extra patrol cars to watch over his house. He did not obtain an order of protection.

He made his fearful plea to the police shortly after his cross-dressing brother – charged with one murder, a suspect in two others, and under suspicion for more – went on the lam to escape a murder charge in Galveston, Texas, where Robert allegedly killed and chopped up elderly Morris Black two years ago today.

Robert Durst’s joy ride ended on Nov. 30, 2001, when he was picked up for shoplifting in Pennsylvania. His trial for Black’s murder began in Galveston last week.

Reached in California, Thomas told me: “I am under a gag order because I’m on the witness list.

“I can’t talk to you – but I wish you well.”

It’s not hard to understand why Thomas lived in terror of his brother.

As I reported exclusively on Friday, authorities now believe that Robert Durst planned to use his time on the lam to take care of unfinished business. They think he plotted to do away with his other brother, Douglas, who runs the Durst family’s multibillion-dollar Manhattan real-estate empire. The two have been estranged since Robert was passed over for the top job in the family business 20 years ago.

Lawmen concluded that Robert planned to do Douglas harm after listening to tape-recorded jailhouse telephone conversations between Robert and his wife, Debrah Lee Charatan, made while Robert was locked up in a Pennsylvania jail between December 2001 and January 2002.

One tape reveals that Robert had driven to Douglas’ house in Katonah, N.Y., armed and dangerous. But he left the driveway without incident, later telling his wife, “I screwed it up.”

Also, in his car were directions to the Connecticut home of another nemesis, Gilberte Najamy, who’s trying to prove that Robert killed his first wife, Kathie, who disappeared in 1982.

The tapes suggest Robert suspected that Thomas was afraid of him. In one jailhouse chat with his sister, Wendy Kreeger, Robert asked, seemingly innocently, why Thomas hadn’t visited him behind bars.

Thomas’ fear was not based on paranoia alone.

While Robert Durst remains a suspect in the disappearance of his first wife, he is also suspected in the 2000 murder of his old friend, Susan Berman, in Los Angeles. Cops believe Robert wanted to shut up Berman because she was about to nail him for Kathie’s murder.

Investigators are just now learning the full extent of Robert Durst’s bizarre lifestyle of the last 20 years. He combed the country, from homeless shelters to luxury hotels, like some kind of wealthy vagrant, assuming the identities of a dozen or more people, male and female.

This year, Durst also came under suspicion for the disappearances of two young California women.

One is Karen Marie Mitchell, who was 16 when she vanished from Eureka, Calif., in 1997. A composite drawing of the last person seen with Karen shows a gray-haired older man with big glasses.

Cops also are looking at any links to the disappearance of college student Kristen Modafferi, 19, who was last seen in a San Francisco coffee shop in 1997.