The highest court in Connecticut will decide the fate of a Kennedy cousin accused of a 40-year-old murder

The Connecticut Supreme Court heard arguments on Wednesday to decide whether to reinstate the 2002 murder conviction of Michael Skakel, a wealthy Kennedy cousin.

Skakel - a nephew of Ethel Kennedy - was convicted of bludgeoning his neighbor, Martha Moxley, to death with a golf club in 1975 when they were both teenagers.

He was freed on a $1.2 million bail in 2013 after Thomas A. Bishop, Connecticut lower-court judge, overturned the murder conviction. Bishop wrote a 136-page opinion criticizing the lawyer who represented Skakel in the 2002 trial.

Bishop ruled that Skakel would likely have been acquitted if Michael Sherman, Skakel's lawyer, had focused more on Skakel's brother Thomas, reports The Associated Press.

Dorthy Moxley, Martha's mother, told reporters that she hoped the court will reinstate Skakel's conviction, according to The Wall Street Journal.

She said that the jury, "could just tell that Michael was guilty," per The Wall Street Journal.

If Skakel's conviction isn't reinstated, Connecticut prosecutors will decide whether to seek a new trial for Skakel.

The strange case against Skakel had no physical evidence and went unsolved for two decades. Skakel's life of privilege was interrupted in 2000, when he was charged in the horrific murder at the age of 39.

In 1975, Moxley was killed just outside her family's house with a 6-iron golf club owned by Michael Skakel's mother Anne Reynolds Skakel. He and his brother Thomas were both suspects in the case, as was a tutor who lived with the Skakels. Nobody was arrested after the 1975 murder, though, and the case went cold for decades.

The case started to heat up again in 1998, after former LAPD detective Mark Fuhrman wrote a book called "Murder in Greenwich: Who Killed Martha Moxley?" Fuhrman theorized that Michael Skakel killed Moxley after he saw her kiss his brother. That same year, the state attorney in Bridgeport, Connecticut convened a grand jury to see if there was enough evidence to prosecute any of the suspects, according to The Times.

Skakel - who had worked with his cousin at a company called Citizens Energy Corporation and as a professional speed skier - was convicted of murder in 2002 despite a lack of physical evidence. The Times reported that the jury heard evidence that he had unrequited romantic feelings for Moxley and access to the weapon used to kill her.