She was sailing near Catalina Island in California with Wagner, and the actor Christopher Walken, on a yacht captained by Dennis Davern.
Wood was discovered in the water about a kilometre from the yacht on the morning of November 29, 1981, wearing a nightgown, socks, and a down jacket. She was 43.
Speculation included reports of blistering rows, a love triangle, and that Wagner was jealous of the younger Walken. An autopsy found bruises on her body, "likely caused by another person", said Corina.
After two weeks the case was closed as "accidental drowning". But in 2011 police began looking into it again.
Walken is not considered a person of interest, because he was asleep at the time. But Wagner, now 87, star of Hart to Hart, told investigators at the time that he believed his wife had taken the dinghy and disappeared, and has since refused to speak to the police, despite several attempts.
"He has always been a person of interest," said Corina. "He is not a suspect, as this is a suspicious death investigation, not a murder investigation.
"There were four people on the boat that night and one of them ended up dead. He was the last person to see her alive. He was in the salon of the boat and said 'Natalie's gone, she's missing'. And then he says 'oh, the dinghy's gone'. No one heard it go off. She doesn't drive. It doesn't make sense."
He said they would love to speak to Wagner, and pointed out curious aspects of his story.
"I know his original story, when he said what happened that weekend – he was in the salon, then checks on her, and she had gone. She never drives; she doesn't know how to."
He also said Wagner did not appear aware of the urgency of the situation, once Wood disappeared.
"When Davern suggests turning the light on, he says no, no. They say let's call for help, he says no, let's wait. Instead he goes and gets drunk.
"We would love to talk to Robert Wagner. You bet. His version of events doesn't add up to what we've found.
"We can't make him. He doesn't want to talk to us."
In his 2009 book, Pieces of My Heart, Wagner wrote that on that outing in November 1981, he became jealous and argued with Wood and Walken. Later, he was unable to find his wife, searched the boat with the captain and noticed the dinghy was missing. Wagner assumed his wife had gone ashore.
In an April 2016 interview with People magazine he said: "We were all so shattered by the loss."
Corina said the greatest challenge was the passing of years, and described the appeal for information as a final attempt to solve the case.
"Our biggest challenge is time," he said. "Some of the witnesses have passed away. The original investigator passed away recently. We're reaching out one last time to see if anyone can shed some light on this.
"We are doing our last shot here to see if anyone else can come forward. When the tips all dry up, we move on to the next case."
This article originally apperaed on the Daily Telegraph.
