February 01, 2018 11:41 AM

Nearly 40 years after Natalie Wood died under mysterious circumstances, Los Angeles County Sheriff’s investigators say her widower Robert Wagner is “more of a person of interest” in the case.

The Hollywood star was married to Wagner twice — first in 1957 (they divorced five years later) and again in 1972 until her death.

RELATED: Natalie Wood: A Hollywood Life Cut Short in Pictures

Though Wagner has largely remained tight-lipped about Wood’s death, he’s opened up in recent years about his family’s heartbreak.

“We were all so shattered by the loss, and we were hanging on to each other,” Wagner told PEOPLE in 2016 for a cover story on her passing. “You just take it moment by moment and hope that it gets better.”

Wood died on Nov. 29, 1981, off of Catalina Island in California. The incident happened while the 43-year-old actress was sailing with her husband on their yacht, Splendour. Christopher Walken, Wood’s then-costar in the movie Brainstorm, and the boat’s captain, Dennis Davern, were also on board.

RELATED: Natalie Wood and Robert Wagner’s Love Story in Pictures

She was found floating facedown in the Pacific about a mile away from the boat, 200 yards off Blue Cavern Point. Two weeks after her death, police wrapped up their investigation after a coroner determined that Wood had a “slightly intoxicated” blood-alcohol level of .14 percent and ruled her drowning accidental. The operating theory: She fell into the water while trying to secure the dinghy.

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In Wagner’s 2008 memoir, Pieces of My Heart, he wrote that after a night of drinking, he got into an argument with Walken over Wood’s career.

At one point, the now 87-year-old actor wrote, “I picked up a wine bottle, slammed it on the table and broke it into pieces.”

As for what caused her to fall off the boat, Wagner wrote it was “all conjecture. Nobody knows. 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.”

In the months following Wood’s death, Wagner said that it was difficult to function.

“When Natalie died, I thought my life was over,” Wagner wrote in his 2016 memoir, titled I Loved Her in the Movies: Memories of Hollywood’s Legendary Actresses. “Luckily I had the help of a great many people who loved her and who loved me as well.”

Looking back, he said, “I thought I would never get up, you know? My children helped me heal. And my friends were so supportive,” he wrote. “And slowly I was able to get up. I got on my feet but it was very, very difficult and a sad time.”

Wagner said he mostly remembers Wood for her fulfillment and joy in being a mother.

Silver Screen Collection/Getty

“Natalie was swept away by motherhood,” he wrote. “It was a total home run for her. She was devoted to our girls.”

Wagner and Wood raised three daughters: Katie, his daughter with his second wife, Marion Marshall; Courtney, his daughter with Wood; and Natasha Gregson Wagner, Wood’s daughter with her second husband Richard Gregson.

“I’m certain because my mom died, my relationship with my stepdad is way deeper than it would have been had she lived, because he had to be my mom and dad,” Natasha told PEOPLE in 2016 of her relationship with Wagner.

But even Natasha recalled seeing the pain in Wagner after Wood’s death.

“Before my mom died, my dad was a happy go lucky person and kind of the life of the party,” she said. “After she died, when I would look at him from a distance, from my bedroom window walking into the house, there was a heaviness and a sadness to him that hadn’t been there before.”

At the time, Wood’s death was classified as an accidental drowning, but the case was reopened in 2011.

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“As we’ve investigated the case over the last six years, I think he’s more of a person of interest now,” Los Angeles County Sheriff’s Department Lieutenant John Corina said in an upcoming interview with CBS’ 48 Hours. “I mean, we know now that he was the last person to be with Natalie before she disappeared.”

Wagner’s attorney didn’t immediately respond to PEOPLE’s request for comment.

Wagner has refused to speak with investigators since they began to look into the circumstances surrounding Wood’s death again.

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

When asked if Wood’s death was a murder rather than a tragic accident, Corina said, “I think it’s suspicious enough to make us think that something happened.”

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