Was the laughing gas dentist scene in The Pink Panther Strikes Again done in a previous movie? Maybe a Jimmy Cagney comedy from the thirties or forties?
I don't think that it was done exactly, and there have been many different scenes with dentists and tooth mishaps.
However if you are thinking it's Jimmy Cagney, there are two possibilities. The first is the original film "The Man Who Knew Too Much", (1934) which was a Hitchcock thriller. This featured a scene in a dentists chair where the dentist is probing around in the hero's mouth and interrogating, only to have the tables turned on him.
The Jimmy Cagney reference is from the remake of the same name in 1956, but in this movie the scene was changed from a dentists office to a taxidermy shop.
If neither of those are correct, here is at least a partial list of movies with dentist scenes in them: Dentist scene list
The movie I was looking for is Pale Face starring Bob Hope. He has the same scene as Sellers, getting goofy on the laughing gas and then pulling the wrong tooth. Blake Edwards' version is much longer and funnier, but Hope and Sellers were different comic actors.