In October 2006, Mark Seal wrote in Vanity Fair that Elkann "had been found naked and unconscious in the apartment of Donato Broco, a 53-year-old transsexual prostitute known as Patrizia." He was brought to the hospital, where he was in a coma for three days. Police investigated him at the time for cocaine use and soliciting prostitution.
On November 27, 2016 in New York, Elkann was arrested for making a false police report claiming that he had been unlawfully imprisoned. He had previously contacted his family, stating that he would "be harmed" if they did not pay a $10,000 ransom. He was accompanied by a transsexual escort who was also arrested. Charges against the escort were later dropped.