“I would get there and the lights are off, and he would say to me after I came in and after a hug ‘take your clothes off,’” the man wrote in a statement to the police.

“On various occasions he would ask me how I touched myself and then he would touch me the way I touched myself,” the man wrote. “I was never able to be aroused by this. But then he would masturbate himself at his bed or in the bathroom.”

The police report contains a college recommendation that Mr. Levine wrote for the man on Met stationery in 1987. In it, Mr. Levine wrote that he had known the teenager for “almost fifteen years.” The man also told the police that Mr. Levine had given him money over the years, which he estimated added up to $50,000.

Peter Gelb, the general manager of the Met, said Saturday night that the company would begin an investigation of Mr. Levine.

“This first came to the Met’s attention when the Illinois police investigation was opened in October of 2016,” Mr. Gelb said. “At the time Jim said that the charges were completely false, and we didn’t hear anything further from the police. We need to determine if these charges are true and, if they are, take appropriate action. We will now be conducting our own investigation with outside resources.”

The Boston Symphony Orchestra, where Mr. Levine was music director from 2004 to 2011, issued a statement Sunday saying that its management “was never approached by anyone in connection with inappropriate behavior” by Mr. Levine and was not aware of the new accusation of sexual misconduct until the news broke Saturday night. Before Mr. Levine was hired as music director in Boston, the orchestra’s management did “a personal and professional review of all aspects” of his candidacy and then moved ahead with his appointment.