NEW YORK, OCT. 27 -- Rumors about Gov. Mario M. Cuomo's supposed ties to organized crime have been circulating on the political grapevine for months, and now, to Cuomo's relief, they are out in the open.

In the current issue of New York magazine, veteran journalist Nicholas Pileggi details the rumors and pronounces the stories "misleading and false." Pileggi writes that they have been "passed around by cops, media people and others in a kind of shadow network of gossip and loose talk."

Pileggi said most of the rumors had been spread by two people, a Long Island public-relations man who worked for the Right to Life candidate in the 1986 gubernatorial campaign and a conservative aide in the state legislature.

Cuomo (D) and his aides said they were relieved that the rumors were reported and knocked down in one account. The governor called the rumors "political garbage distributed by political garbage dealers" and said that was "a price I pay for being an Italian American." He thanked "members of the media who recognized this ugly effort for what it was."

Cuomo raised the issue earlier this month when he called a New York Times reporter and said there seemed to be an "organized" campaign of rumors that he had decided not to run for president because of past misdeeds by his family. He would not elaborate on the rumors.

The story was amplified when Lesley Stahl of CBS News asked Cuomo on "Face the Nation" about "skeletons in his family closet." The rumors also have been pursued by several other news organizations, some of which, according to Pileggi, have hired private detectives.

In the magazine piece, Pileggi, who has covered organized crime since 1956, reported these rumors:That Cuomo's father-in-law, Charles Raffa, now 83, was the victim of a mob beating that grew out of a dispute about arson.

Raffa, who owns several buildings and vacant lots in Brooklyn, was severely beaten in 1984 after he showed an empty supermarket in East New York to a potential buyer. Police did not catch the assailant but found no evidence of mob involvement or planned arson, Pileggi said. Andrew Cuomo, the governor's son and campaign manager, is quoted as dismissing suggestions of arson because the supermarket had no fire insurance. That Cuomo interfered with the police investigation of the beating and that an arrest of Raffa for arson was erased from state computers. Cuomo was in Albany on the day of the attack, Pileggi reported, and state police have a computer record of a 1973 arrest of Raffa, but on a misdemeanor charge of offering an illegal gratuity. The charge was later dismissed. That Cuomo once represented organized-crime figures as a Queens lawyer. Pileggi found only that Cuomo once represented an association of about 15 junkyards, one of which was partially owned by Joseph (Joey Narrows) Laratro, a member of the Luchese crime family. Cuomo was quoted as saying he never represented Laratro personally and that he "got stiffed on the fee." That a mobster gave Cuomo $30,000 in political donations. At a 1984 fund-raiser, Cuomo's campaign received a $1,000 check from each of five firms that investigators have identified as paper companies set up to avoid paying gasoline taxes. The campaign gave the money to charity after this was discovered, according to Andrew Cuomo. That Cuomo's former law firm passed money to a mobster later acquitted of murdering a detective in Queens. Pileggi found no evidence of this.

Gary Fryer, Cuomo's press secretary, said today that "the most dangerous part of the whole thing is it was amorphous. What really incensed Cuomo was the idea that if you really want to go after an Italian American, all you have to do is say the M word {Mafia}, and he would instantly be put on the defensive and have to prove to the world it isn't true. That irked him. It touched a chord."

Fryer said the governor was pleased at the "vindication," but also concerned that "two clowns can shoot off their mouths in a reckless way and harm someone and his family."