The US Supreme Court refused today to resurrect a lawsuit filed against the FBI by relatives of Edward “Brian’’ Halloran, who must now turn to Congress where Bay State lawmakers have filed special legislation to compensate them for Halloran’s death in 1982, allegedly at the hands of James “Whitey’’ Bulger.

“It’s disappointing, but the Supreme Court takes very few cases,’’ said William E. Christie, the New Hampshire-based attorney for the Halloran family. “Once again, the courts have denied the Halloran family justice.’’

The court’s decision not to hear the case came in a 16-page order that listed dozens of other cases from around the country. The newest member of the US Supreme Court, Justice Elena Kagan, did not participate in the decision, the court said.

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Halloran’s relatives won a $2 million US District Court verdict against the FBI because of its corrupt relationship with Bulger. But the First US Circuit Court of Appeals overturned that verdict, ruling that the statute of limitations had expired.

Halloran, a 41-year-old Bulger associate, was getting a ride home from a bar on Boston’s waterfront on May 11, 1982, when Bulger and an unidentified associate allegedly opened fire, killing him and the man who gave him the ride, Michael Donahue, a 32-year-old Dorchester truck driver.

Bulger allegedly acted because he had been tipped off by a corrupt FBI agent that Halloran had become an FBI informant. Bulger himself was an FBI informant who allegedly used his protected status to his advantage during a ruthless reign in Boston’s underworld.

Today’s ruling ends the litigation for the Halloran family. But the legal battle continues for the Donahue family, which did not seek to appeal to the Supreme Court.

Boston attorney Edward Hinchey, who represents the family, said the family, taking a different legal tack, will ask a federal judge Wednesday if the family can continue its lawsuit against four former FBI officials for civil rights violations,

Hinchey said that if the family loses its bid Wednesday, “then we are all probably in front of Congress.’’

Bulger’s long-time sidekick and fellow informant, Stephen “The Rifleman” Flemmi, testified during court proceedings that former FBI agent John J. Connolly Jr. warned him and Bulger that Halloran was cooperating with the FBI and had implicated the gangsters in an earlier slaying.

Flemmi said the tip prompted Bulger to kill Halloran and that Donahue, who was simply giving Halloran a ride home, was just an innocent bystander

Bulger is awaiting trial on federal racketeering charges that include allegations he killed 19 people, including Halloran and Donahue.