‘What Ever Happened to That Gap-Toothed Guy?’ : Television: David Letterman leaves NBC tonight for rival CBS, which may be why he isn’t getting the ‘Cheers’ farewell treatment.

David Letterman is threatening to get a little sentimental tonight on his last night on “Late Night” on NBC. But don’t expect NBC to return the sentiment.

While both sides say that the parting is amicable, NBC is not promoting the final episode of “Late Night With David Letterman” the way the network eulogized the finale of “Cheers.” Letterman, after all, is crossing the street--and a highly publicized street-crossing it is--to compete with NBC’s “Tonight Show” on CBS, beginning on Aug. 30.

As of Thursday, NBC was planning no official send-off on the air during the final program, which marks the end of Letterman’s 11 years on NBC. No NBC executives were planning to attend the final taping, according to an NBC spokesman, although NBC president Bob Wright planned to come backstage during Thursday night’s taping to offer private congratulations and goodbys to Letterman.

Letterman’s producers admitted that they were upset about NBC’s corporate attitude. “We are going to do a great show on Friday night, and I’m sure Dave will say a nice goodby to NBC and to all of the NBC people who are not coming with us to CBS,” said Robert Morton, executive producer of “Late Night.”

In recent weeks, NBC has taken the step of removing Letterman’s name and face from “Late Night” promos on the network. NBC owns the “Late Night” name and, beginning in August, may use that title for its own new late-night host, Conan O’Brien.

“We’re very appreciative of NBC’s support over the years,” Morton said, “but basically it seems as if they’re letting us go gently into the night. We don’t want to make a big deal out of our departure because we are going to CBS. But what NBC has been doing in the past few weeks does bug me because we have not shied away from our commitment. We’ve still been here, having great shows and great guests.”

NBC officials said that they were not attempting to bury Letterman’s departure. “Letterman’s producers are in charge of creating the final show,” noted NBC spokesman Curt Block. “And even they have noted that this is not an easy situation because Letterman is leaving to go up against Jay Leno on ‘The Tonight Show.’ ”

Letterman--who has had both Tom Brokaw and Katie Couric as guests on “Late Night” in the past two weeks--will be interviewed today on both “Today” and “NBC Nightly News.” But sources said that Letterman’s producers initiated the “Today” booking. “You have to make a distinction between the creative types here and the ‘suits,’ ” said one source on the Letterman show. “NBC isn’t being aggressively negative about Letterman’s departure, but they’re not exactly stepping up to the plate to say goodby.”

Letterman, who has made a career out of zinging NBC and its corporate parent, General Electric, in his years on “Late Night,” has been satirizing his own “going out of business” sale on NBC this week.

For tonight’s show, the producers have booked actor Tom Hanks, plus a surprise mystery guest whose identity they will not divulge. The producers indicated that there are likely to be some sentimental surprises for Letterman from the staff of the show. In addition, there will be clips from some of Letterman’s shows in the past.

Demand for tickets in recent months has been about three times as high as usual, Block said, and no seats have been available for the final two weeks’ shows “for months.”

Once the curtain comes down at NBC tonight, Letterman and his staff, most of whom are moving with him to CBS, will not be going on vacation. Stressing that Letterman’s CBS show will be essentially the same show he’s been doing on NBC, producer Morton said, “Monday morning, we’ll begin having meetings about bookings, writing and other parts of the CBS show. There’s no rest for the restless.”