Parole was denied Wednesday morning for Kennedy cousin Michael Skakel.
Skakel is currently serving 20 years in jail for beating 15-year-old Martha Moxley to death in Greenwich.
At the parole hearing at the McDougall-Walker Correctional Institution, Skakel, 52, spoke slowly to the board.
"I know the best chance of me getting parole is admitting guilt in this crime," Skakel said. "Ten and a half years later, I cannot do that. I did not commit this crime."
In 2002, Skakel was convicted of killing his neighbor in 1975. Prosecutors said he beat Moxley to death with a golf club in Greenwich when they were both 15 years old.
"He's never taken any responsibility," said John Moxley, who is Martha's brother. "He's never shown any remorse. He's still looking for loopholes."
Skakel told the board members that he wanted the chance to be with his 13-year-old son, while his ex-wife battles cancer.
"That's extremely stressful, knowing that as his father I can't be there, to comfort him when his mother's not doing well," Skakel said.
Officials said the parole board has received dozens of letters in support of Skakel, including one from his cousin, Robert F. Kennedy Jr.
"I pray to God and to Martha, whoever did this crime is brought to justice because the Moxleys deserve closure. It just isn't me," Skakel said.
Dorothy Moxley, the victim's mother, rejected Skakel's claims of innocence.
"Martha, my baby, will never have a life," she said. "One thing Michael has not shared with me, but I can tell him to lose a child is the worst thing in the world. I pray nothing happens to your child."
Skakel's family has never given up trying to get the conviction overturned. His family will return to court in just a few months to seek a new trial.
"We've basically been dragged through the mud for several decades, so as you can imagine that certainly takes a toll, and it rips at the fabric of any family," said John Skakel, who is Michael Skakel's brother.
In addition, Michael Skakel filed a defamation lawsuit against CNN's Nancy Grace after alleging she made false statements about some of the evidence of Michael Skakel's DNA near the crime scene.
Michael Skakel's next parole hearing was set for October 2017.
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