TALK-SHOW host David Letterman has been recorded on tape having sex with a female staff member - and he is worried that the footage will eventually be leaked, it's reported today. Letterman, 62, recently admitted to having a series of sexual relationships with some of the women that work for him. The chat show host and a much-younger female co-worker have apparently been captured on a studio surveillance tape in a compromising position. “If the tape makes its way into the criminal case, it’ll explode his marriage to smithereens,” a source told the National Enquirer magazine.