Letterman told his story during a taping of his late-night show, mixing in jokes to an audience that seemed confused about what it was. He called it a "bizarre experience" that left him feeling disturbed and menaced.
In a release from the show's production company, Letterman said he referred the matter to the Manhattan district attorney's office. An investigation ended in an arrest Thursday after Letterman issued a phony $2 million check to keep the matter silent.
The network said late Thursday the person who was arrested works on "48 Hours" and has been suspended pending the results of the investigation.
The late-night comic began his show by walking onstage and briefly leaning on a pillar with his back to the audience. Then he gave a monologue with jokes against frequent foils like Dick Cheney and Sarah Palin. He told his personal story after sitting behind his desk.
He said he was glad the audience was in a pleasant mood "because I have a little story that I'd like to tell you and the home viewers as well."
Three weeks ago, Letterman said he got in his car early in the morning and found a package with a letter saying "I know that you do some terrible, terrible things and that I can prove you do some terrible things." He acknowledged the letter contained proof.
Letterman said he called his lawyer to set up a meeting with the man, who threatened to write a screenplay and a book about Letterman unless he was given money. There were two subsequent meetings with the man, the last one resulting in the check being delivered.
He told the audience that he had to testify before a grand jury on Thursday.
"I was worried for myself, I was worried for my family," he said. "I felt menaced by this, and I had to tell them all of the creepy things that I had done."
"The creepy stuff was that I have had sex with women who work for me on this show," he said. "My response to that is yes, I have. Would it be embarrassing if it were made public? Yes, it would, especially for the women."
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