A Hollywood glamour couple spent the night on a yacht. Only one made it back to shore.

It’s a mystery that has transfixed Hollywood for almost 40 years.

On November 29, 1981, actress Natalie Wood drowned while on a boat trip off California with her husband, film actor Robert Wagner.

At the time, her death was ruled as an accident, but questions have always lingered.

And now, in a new documentary, which will air on CBS  in the United States, Los Angeles County Sheriff’s Lieutenant, John Corina, says he considers Wagner a ‘person of interest’ in the case.

“I haven’t seen him tell the details that match all the other witnesses in this case. I think he’s constantly changed his story a little bit. And his version of events just don’t add up,” he says.

Listen: Holly Wainwright and the Stephens Twins explore our obsession with true crime: is it simply our love of a good story, or something more sinister? (Post continues after audio…)

So what do we really know about what happened that night?

It was Thanksgiving weekend. Wood, who starred in West Side Story and Rebel Without a Cause, was aboard her family’s yacht, Splendour, with Wagner and their guest, Christopher Walken – Wood’s co-star in the movie Brainstorm at the time.

Dennis Davern was skipper of the 60ft luxury vessel on its trip off Santa Catalina Island in California.

On the Saturday night, November 28, the group enjoyed a boozy dinner at the upscale restaurant, Doug’s Harbour Reef, before returning to the boat where they continued to drink heavily.

This is where things get rather murky.

At around midnight, Wood was discovered missing from the boat. The following morning, the 43-year-old, who was said to have a lifelong fear of open water and drowning, was discovered floating around a mile away. She was dressed in a flannel nightgown, knee-high socks and a red down jacket, and was covered in bruising.

The initial investigation concluded that Wood had slipped and fallen in the water, and died of hypothermia.

Natalie Wood was at the height of her career when she drowned in 1981. Getty

But the couple's troubled relationship - they'd married twice and were known to argue - led people to draw other conclusions.

The investigation was reopened in 2011 after Davern said he'd lied about that night and claimed that the couple got into an explosive argument. When asked at the time by NBC News if he thought Wagner was responsible for Wood's death, he replied: "Yes, I would say so. Yes."

The following year the Los Angeles Coroner’s Office changed the cause of death on Wood's death certificate from accidental drowning to “drowning and other undetermined factors.”

So while they weren't saying foul play was a factor, they weren't ruling it out either.

Since then, the Los Angeles County coroner released a report, contrary to the original autopsy, which stated some of the bruising on Wood's body could have occurred before the drowning.

The report said: "The location of the bruises, the multiplicity of the bruises, lack of head trauma, or facial bruising support bruising having occurred prior to the entry into the water."

Wagner, now 87, has always denied any involvement in Wood's death, concluding in his 2008 memoir, Piece of my Heart, that "nobody knows" how she fell off the boat. In the book, he admits there was an argument - although he says it was between him and Walken.

He wrote: "There are only two possibilities: either she was trying to get away from the argument, or she was trying to tie the dinghy. But the bottom line is that nobody knows exactly what happened."

There are so many unanswered questions. If Wood had a lifelong fear of drowning, why would she try to leave the yacht in the middle of the night? Why has Wagner refused to speak to investigators since 2011? Davern swears there was an argument between the couple - could this be what led to Woods' death?

Now it seems, six year after reopening the case, despite Wagner's refusal to talk to them, investigators are getting closer to the truth.