Moxley was beaten to death with a golf club on Oct. 30, 1975. Her body was found the next day on her family's Greenwich estate.
Thomas Skakel, then 17, and his brother, Michael, then 15, have been identified by authorities as suspects in Moxley's killing.
Murphy's firm was hired in 1991 as the Skakel family attempted to gather evidence to prove the boys' innocence.
However, a Sutton report, described in a story in Newsday in 1995, revealed that both brothers had changed their stories about their movements the night of Moxley's murder, giving different accounts than they gave to police in 1975.
Murphy, testifying Wednesday at the Nassau County Courthouse in Mineola, N.Y., said he was hired by attorneys for Michael and Thomas Skakel, and therefore any work he did is protected by attorney-client privilege.
Murphy told Judge Jerald Carter that if he is forced to testify before the grand jury, it could potentially ruin his business because his clients expect confidentiality.
"Everything he did was with the clear understanding that it was to be privileged and remain confidential," said Robert Gottlieb, an attorney representing Michael and Thomas Skakel on the privilege issue.
But Connecticut prosecutors, in court papers, said Sutton Associates was retained by Rushton Skakel Sr., the father of Thomas and Michael.
They said that Murphy's testimony is important to the grand jury because he participated in interviews of Michael and Thomas in which both boy significantly changed their stories.
Thomas Skakel originally told police he went inside to do homework after leaving Martha at 9:30 p.m. He later told Sutton investigators that he and Martha spent another 20 minutes together, kissing and fondling each other to the point of masturbation, according to the Newsday report.
Michael originally told police he saw Moxley at his house early in the evening, but left his house at about 9:30 p.m. to go to his cousin's house. He said he went to bed after returning from his cousin's house at about 11:20 p.m.
But in 1992, Michael told Sutton Associates that he went outside after returning home. He said he climbed a tree near the Moxley home, yelled at a window he thought was Martha's bedroom, then masturbated in the tree.
In his testimony Wednesday, Murphy said he had never participated in an interview or had any conversation at all with Michael Skakel. He said he had participated in an interview of Thomas Skakel.
Judge Carter said he will issue his decision within a week on whether Murphy will be compelled to go to Connecticut to testify before the grand jury.
Willis Krebs, a former Sutton investigator, is also fighting a subpoena. A judge in Suffolk County, N.Y., will hear arguments in that case on Dec. 15.
The Skakels lived near the Moxleys in the exclusive Belle Haven section of Greenwich. The boys' father, Rushton Skakel, is the brother of Ethel Kennedy, Robert Kennedy's widow.
Both Thomas and Michael Skakel have denied any involvement in Moxley's death.
The 6-iron used to kill her was matched by police to a set owned by the Skakel family.
AP-ES-12-02-98 1840 EST
Copyright - Associated Press.