Letterman said that “this whole thing has been quite scary.” But he mixed in jokes while outlining what had happened to him, seeming to confuse a laughing audience at Thursday’s taping about whether the story was true.

The network said the person who was arrested works on the true-crime show “48 Hours” and has been suspended. A person with knowledge of the investigation said the suspect is Robert J. Halderman. The person spoke on condition of anonymity because authorities have not released the suspect’s name.

A “48 Hours” producer named Joe Halderman was part of a team nominated for an Emmy for outstanding continuing coverage of a news story in a news magazine in 2008. Two numbers listed for Halderman were disconnected, and a message left at a third number was not immediately returned Thursday.