NORWALK, Conn. – In a case that could open a window onto a world of wealth and influence, Kennedy cousin Michael Skakel went on trial Tuesday in the 1975 murder of a teen-age neighbor, with prosecutors saying he admitted to the crime in the 27 years since.

Skakel, 41, is accused of beating Martha Moxley to death with a golf club in the rich community of Greenwich when both were 15.

In opening statements, prosecutor Jonathan Benedict told the jury it will hear from several witnesses who talked with Skakel about the killing, which occurred on Mischief Night, the night before Halloween.

“Some people can’t keep a secret, as it turns out he’s been talking about his night of mischief since at least the spring of 1978,” Benedict said. He said the evidence would include both explicit and partial admissions.

“Some of these partial admissions may seem innocent and ambiguous,” but taken together they will show Skakel committed the crime, he said.

The defense warned the jury not to get caught up in the emotions of the case and said the physical evidence against Skakel was “zilch.”

“You’ll see they have a lot of pieces of a jigsaw puzzle,” defense attorney Michael Sherman said. “But the problem is, the jigsaw pieces don’t fit.”

The case went unsolved for years, giving rise to suspicions that wealth, privilege and the Kennedy connection had somehow protected Skakel. But the slaying regained attention after several books were written about it.

The prosecutor told the jury that it will hear evidence that the Skakel family made a “concerted effort” to hide Skakel’s guilt from police. Skakel is the nephew of Ethel Kennedy, the widow of Robert F. Kennedy.

The passage of time has done much to cloud the high-profile case. Two key witnesses have died, and investigators have grown old and retired. There are no eyewitnesses to the killing and limited forensic evidence.

Skakel, who has grown from a pudgy teen with drug problems into a divorced father and recovering alcoholic, did not comment as he entered court Tuesday. None of his Kennedy relatives showed up for the first day of testimony.

The case took a long and twisting path to reach the courtroom, with Skakel arrested two years ago after an investigation by a judge acting as a one-man grand jury. Skakel’s lawyers had argued that he should be tried as a juvenile, which could have meant no punishment at all if he had been convicted, since he is too old to be sent to a juvenile prison.

The case was transferred instead to adult court. If convicted, Skakel could get life in prison.

Moxley’s body was discovered beneath a tree on the family’s Greenwich property, beaten with a golf club that investigators said matched a set in the Skakel household.

The victim’s mother and brother, Dorthy and John Moxley, were the first two witnesses called Tuesday. They described their frantic efforts to find Martha.

Dorthy Moxley said she went to the Skakel house Halloween morning looking for Martha, and Skakel opened the door. She said he appeared “hung over.”

Sherman questioned Moxley about statements to authorities in which she said she heard barking dogs and teen-age voices the night of the killing. Moxley said she could not recall whether she told authorities she had heard Martha’s voice.

“After Martha died, I was like a zombie,” she said. “I just barely functioned.”

The Moxleys left the courthouse just before graphic pictures of the crime scene were shown. John Moxley said the family would not return to the trial until all the forensic evidence had been presented.

“We just don’t need to see that,” he said.

Prosecutors have more than 40 potential witnesses, including some who allege Skakel confessed to the crime when they attended a substance abuse facility with him in Maine in the late 1970s. Skakel’s defense list has about two dozen witnesses, including several from the same facility.

Kenneth Littleton, who started his job as a live-in tutor for the Skakel family the day of the slaying, is expected to take the stand later in the week. Skakel’s lawyers have alleged Littleton confessed to the crime, but the judge has not yet ruled whether the statements can be used.