The manager, who was also charged with drink driving, then reportedly drove off with the auto before being stopped by police.
The Canadian Olympic Committee confirmed on Saturday that members of the national team were under police investigation.
The group were met with a frosty reception when stopped by police less than hour later, with all three found inside intoxicated, South Korean police said. The manager has been charged with drunken driving, the official said.
Duncan and his wife released a statement, apologizing for the incident in a press conference on Saturday.
"We can confirm that an incident occurred", said Overholt.
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The indictment accuses him of taking a compromising photo of the woman without her consent during a sexual encounter at his home. Louis TV station KMOV an audio recording of her confessing the affair and accusing Greitens of threatening to blackmail her.
A South Korean police source told CNN that Raine, the driver, had a blood alcohol level of 0.162 when tested one hour after stealing the vehicle.
Technical coach William Raine called his actions "inexcusable".
Duncan, who started skiing at the age of 3, switched from alpine to ski cross - a timed freestyle event on a course made of both natural and man-made features - and placed 8th in the final this week.
A Canadian Olympian might have gone a little too far in his post-Olympic celebrations in PyeongChang. "I would also like to apologize to the owner of the vehicle that was involved". We are deeply disappointed in the behaviours in these individuals. "We engaged in behavior that demonstrated poor judgment and was not up to the standards expected of us as members of the Canadian Olympic Team or as Canadians", the statement from David and Maja Margrethe Duncan read.
Canada have not identified the trio but the athlete is understood to be a ski cross competitor and the police released the ages and nationalities of all three suspects - two Canadian men, aged 35 and 48, and a 32-year-old American woman.