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Actor Robert Wagner is now considered a “person of interest” in the drowning death of actress Natalie Wood more than 36 years ago, according to a new report.

Los Angeles County sheriff’s officials want to interview Wagner, 87, again about the circumstances surrounding Wood’s mysterious death in November 1981, investigators told CBS’s “48 Hours.”

The 43-year-old Hollywood star was on her family’s yacht — named the Splendour — off Catalina Island in California on Thanksgiving weekend with her husband, Wagner, actor Christopher Walken and Capt. Dennis Davern before she somehow ended up in the water and drowned.

Wood’s death was initially ruled an accident, but her death certificate was amended in 2012 to change her cause of death from drowning to “drowning and other undetermined factors,” adding yet another layer to one of Tinsel Town’s most enduring mysteries.

“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 Lt. John Corina told CBS News of Wagner. “I mean, we know now that he was the last person to be with Natalie before she disappeared.”

The original detective assigned to the case, as well as Wagner and Walken, have all repeatedly said that they considered Wood’s death an accident, but the witnesses’ accounts have changed over time — a problematic aspect, according to Corina.

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

Asked if he thought Wood was murdered, Corina said: “I think it’s suspicious enough to make us think that something happened.”

Wagner has refused to speak with investigators since the case has been reopened. Walken, in contrast, has met with authorities, although it was not clear what Walken may have told investigators.

Wood’s death certificate was amended in part due to unanswered questions about bruises on her upper body, although coroner’s officials stated in a 10-page addendum to her autopsy report that some of them may have occurred before she went into the water, although that couldn’t be definitely determined.

To at least one detective in the case, the circumstances leading up to Wood’s death are less murky.

“She looked like a victim of assault,” Los Angeles County Sheriff’s Department Detective Ralph Hernandez told CBS News. “ … We have not been able to prove this was a homicide. And we haven’t been able to prove that this was an accident, either. The ultimate problem is we don’t know how she ended up in the water.”

“Natalie Wood: Death in Dark Water” will air Saturday at 10 p.m. on CBS.