David Letterman, who built his career skewering philandering politicians and show business “weasels” and “boneheads”, finds himself in the middle of his own celebrity scandal, after he admitted having multiple affairs with employees of his production company, Worldwide Pants.

For the intensely private Letterman, the revelations, which resulted from a bizarre extortion attempt, are sure to be extremely embarrassing, as he tries to extend his lead in the late-night contest. “I have had sex with women who work for me on this show,” he told his audience on Thursday night, calling himself “creepy.”

More seriously, they raised questions for both his company and CBS about whether his actions constituted sexual harassment or at least abuse of a power relationship over employees.

A central figure in the case — one of the women who had a sexual relationship with Letterman — is Letterman’s longtime personal assistant, Stephanie Birkitt, who also often appeared on the air. The sexual relationships had ended before Letterman was married in March, a Worldwide Pants executive said.

For CBS, the episode is doubly embarrassing. The network has been put in a precarious position of trying to steer clear of fallout from some highly questionable activities engaged in by its biggest star, who is experiencing his biggest surge in popularity (and ratings) in years.

The man accused in the case, Robert Joel Halderman, known as Joe, who until last month shared a residence in Connecticut with Birkitt, is a longtime and well-respected producer for the CBS News programme 48 Hours Mystery.

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