From the recording at the Internet Archive:


KEEP YOUR UNDERSHIRT ON
Words by Bert Kalmar, music by Harry Ruby.
As recorded by Ben Pollack and His Park Central Orchestra, with vocal refrain by Burt Lorin, on Victor 22267-A, 1929.

Curb your emotion; don’t go off your nut.
I’ve got a notion I could love you, but
Don’t get excited; keep your undershirt on.

Maybe I’ve got stuff you admire, sis.
Baby, I’m hot stuff, so remember this:
Don’t get excited; keep your undershirt on.

I always let the girls kiss me
If they like it (Oh!), and they love it. (Oh!)
After I leave them, they’re total wrecks.
Oh, baby, I’m just full of sex.

Though you’ll upset me, that’s the chance I’ll take.
Go on and pet me, but for heaven’s sake
Don’t get excited; keep your undershirt on.

- - -
The song was written for the musical comedy “Top Speed” which was performed as a Broadway play in 1929 and as a film in 1930. In the play, it was sung as a duet by Lester Allen and Ginger Rogers; in the film it was sung by Joe E. Brown and Laura Lee; however, it was cut before release in the United States.

The song’s lyrics are printed in the published script of the play “Animal Crackers” starring the Marx Brothers. “Animal Crackers” was performed as a play in 1928 and adapted as a film in 1930. According to the script, it was to be sung as a duet by Captain Spaulding (played by Groucho Marx) and Mrs. Rittenhouse (played by Margaret Dumont). However, I do not find “Keep Your Undershirt On” listed in any description of the play or the film.