The Italian called his family from New York to demand a $10,000 ransom “to guarantee his safety”, an official told the Associated Press.
Having found him in Manhattan, investigators now believe Lapo Elkann, 39, concocted the story after he ran out of money following a drink and drugs binge.
The grandson of Fiat’s Gianni Agnelli is now due in court in January.
Lapo Elkann, who was arrested on a misdemeanor charge of falsely reporting an incident, had only arrived in the US last week.
He had told his Instagram followers he was going abroad to pursue “a lot of projects in development… a lot of new ideas” in a rambling video posted on November 24.
Lap Elkann, dressed in a bright red suit, also said the business trip would bring him into contact with “many very interesting characters”.
Instead, media reports in the US and Italy say Lapo Elkann spent two days with the woman, before calling his family in order to get more money.
He claimed he had been held in a Manhattan flat from about 17:00 local time on November 25, until police arrested him outside a public housing complex at about 02:00 local time on November 26.
Lapo Elkann, who was born in New York, is a Fiat shareholder but has no official role in the company.
Instead, the Fiat heir – who made headlines in Italy in 2005 after he was hospitalized for a drug overdose in Turin – runs a company called Italia Independent.
Lapo Elkann has not yet returned a message seeking comment from AP. His publicist, Alessia Margiotta Broglio, declined to comment.
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