The New York City Police Department's longest-running unsolved missing-persons case — the bizarre and legendary disappearance of Judge Joseph Force Crater — may finally be solved.

Judge Crater (search) — who vanished mysteriously 75 years ago — was killed by a city cop and his cab-driver brother and buried under the boardwalk in Coney Island, according to a handwritten letter left behind by a Queens woman who died earlier this year.

"Good Time Joe" Crater was a dapper, 41-year-old judge known for his dalliances with showgirls and his ties to corruption-ridden Tammany Hall (search) — until he got into a cab in Midtown Manhattan one evening in 1930 and disappeared, earning the title of "the missingest man in New York."

The case triggered one of the most sensational manhunts of the 20th century — one that had city detectives fielding more than 16,000 tips from around the country and the world, all of them unsubstantiated.

Although he was declared legally dead in 1939, and his case — Missing Persons File No. 13595 — was officially closed in 1979, Crater's vanishing act has continued to intrigue professional and armchair detectives, clairvoyants and mystery buffs around the globe.

"Pulling a Crater" became slang for vanishing without a trace. But perhaps now, a trace will be found.

Sources told The Post that the NYPD Cold Case Squad is investigating information provided by Stella Ferrucci-Good of Bellerose, Queens, who died on April 2, leaving behind what may be a key to the mystery.

It's a handwritten letter in an envelope marked "Do not open until my death" that her granddaughter Barbara O'Brien found in a metal box in her grandmother's home, the sources said.

In the letter, Ferrucci-Good claimed that her late husband, Robert Good; an NYPD cop named Charles Burns; and the cop's cabby brother, Frank Burns, were responsible for Crater's death.

She added that the judge was buried in Coney Island, Brooklyn, under the boardwalk near West Eighth Street, at the current site of the New York Aquarium (search).

The metal box also contained yellowed clippings about Crater's disappearance, with scribbled notations in the margins.

In her letter, Ferrucci-Good also claimed that Officer Burns was one of the cops guarding notorious Murder Inc. killer Abe "Kid Twist" Reles (search) when he somehow plummeted to his death from the sixth-floor window of a Coney Island hotel in 1941.

Reles had become a mob informant to escape the electric chair, testifying against a slew of Murder Inc. (search) killers. His suspicious death plunge came just hours before he was due to rat out mob boss Albert Anastasia (search).

O'Brien's father, William St. George, said the police told family members that five bodies were found when the aquarium was built. Police sources confirmed that skeletal remains had been found there in the mid-1950s. They said those remains are now being examined to see if they can be linked to Crater.

Police sources also confirmed that a police officer named Charles Burns served with the NYPD from 1926 to 1946, and that he spent part of his career assigned to the 60th Precinct in Coney Island.

O'Brien, who lives in Valley Stream, N.Y., doesn't know what to make of the letter and its claims.

When she found it, she said, "I thought it was a joke and I laughed and I gave it to police."

"I don't know if it's fact or fiction," she said, refusing to show The Post the letter or to say anything more about it.

But "the police were very interested in it," her father noted.

Asked if Ferrucci-Good had been obsessed with the Crater case, St. George said he couldn't recall her ever mentioning it.

Ferrucci-Good was 91 when she died in April. Her husband, Robert Good, a Parks Department supervisor and lifeguard, died in 1975.

Crater had been appointed to the state Supreme Court bench by then-Gov. Franklin D. Roosevelt just four months before disappearing on Aug. 6, 1930.

A few days earlier, while vacationing with his wife, Stella, at their summer cabin in Belgrade Lakes, Maine, he received a mysterious phone call that left him visibly upset. He never told his wife who called.

He left the next day for the city, telling her only that he had to "straighten those fellows out."

He stopped by their Fifth Avenue apartment and gave the maid the next few days off.

He spent the morning of Aug. 6 in his courthouse office, hastily going through his personal files.

He cashed two checks totaling $5,150, took another $20,000 — close to a year's salary — from campaign funds, and left for home with two locked briefcases.

He was last seen at 9:15 p.m. leaving Billy Haas' Chophouse at 332 W. 45th St. with two friends. He said he was going to the theater.

He climbed into a cab nattily dressed in a brown pinstripe suit, gray spats and a straw Panama hat — and that was the last anyone ever saw of him.

Could the cabby have been Frank Burns, brother of Officer Charles Burns? That's one of the questions cops are now grappling with.

It was four weeks before Crater was reported missing.

Friends and colleagues thought he was vacationing with his wife; his wife thought he was away on business. His disappearance was front-page news across the country — leading to reported sightings in every state and scores of foreign lands.

He was reported seen riding a burro and prospecting for gold in California, herding sheep in the Pacific Northwest, locked up in a Missouri mental hospital, shooting craps in Atlanta, working on a steamer in the Adriatic, and running a bingo game in Northern Africa.

His name became a punch line that guaranteed laughs for comics: "Judge Crater, call your office."

Mad magazine published a cartoon showing Lassie finding Crater.

A judge portrayed on TV in a episode of "The Dick Van Dyke Show" assured the sitcom's stars that he wasn't that Judge Crater — he spelled his name "K-r-a-d-a."

There were dozens of theories about his disappearance: He had amnesia; he committed suicide; he ran off with a showgirl; he was rubbed out so he couldn't testify about Tammany Hall corruption; he died in the arms of a prostitute and it was being covered up; he was killed when he didn't pay a blackmailer.

At one point, gangster Jack "Legs" Diamond's name surfaced as his possible killer.

An Albany professor said he believed Crater had been dispatched by the notorious murderer in the basement of an upstate brewery.

Crater's wife remembered his disappearance every year for the rest of her life by visiting a bar in Greenwich Village on Aug. 6.

She'd sit by herself, order two drinks and down one — after saying, "Good luck Joe, wherever you are."

If the letter left behind by Ferrucci-Good is right, he's been sleeping with the fishes all these years.