According to reports, 39-year old Lapo Elkann had spent around a week in New York City before contacting a member of his family, requesting the transfer of a US$10,000 ransom "to guarantee his safety", United States officials reported said.
Police sources told New York Daily News that while there he called a 29-year-old transgender woman who allegedly works as an escort and had contacts to get drugs.
But police sources said Elkann spent much of the weekend holed up in a housing project on the East Side of Manhattan, drinking and doing drugs with an escort.
The official wasn't authorized to discuss the ongoing case and spoke on condition of anonymity.
He was charged with falsely reporting an incident on Sunday, and received a ticket to appear for an arraignment, the Daily News reported. The Agnelli family's investment holding Exor had no comment.
Lapo Elkann, pictured at an event in Madrid in October, allegedly told a family rep he had been kidnapped and needed £8,000 ransom Who is Lapo Elkann? In 2011, he orchestrated the collaboration between Gucci's then-creative director, Frida Giannini, and Fiat on the Gucci Special Edition Fiat 500.
He and his brother Fiat Chrysler chairman John Elkann, are heirs to Italy's biggest industrial dynasty and his holdings in the auto giant make him worth billions.
Elkann almost died in an overdose in 2005 while he was in the apartment of a transgender prostitute in Turin, Italy, the New York Times reported. After his grandfather died in 2003, Elkann became the public face of Fiat, and a controversial one known for bragging about his fabulous life of private planes and luxury cars.
The Italian had only arrived in the USA last week, after posting a rather rambling video on his Instagram account claiming he would be pursuing "a lot of new ideas" and meeting "many very interesting characters". Shares in Italia Independent lost seven per cent of their value Tuesday.