There are two Rodgers and Hart songs with this title, and they have different words and music.
The first version, MGM Song #247, is dated June 9, 1933, and was registered for copyright as an unpublished work by Metro-Goldwyn-Mayer, June 20, 1933.
The second version (a waltz), MGM Song #295, is dated August 4, 1933, and was registered for copyright as an unpublished work by Metro-Goldwyn-Mayer, August 16, 1933.
Neither of the two Rodgers and Hart "Dancing Lady" songs was used in the film.
"My Dancing Lady," introduced by Art Jarrett and danced by Joan Crawford and chorus, was written by Dorothy Fields and Jimmy McHugh.

VERSE
You remember me,
I'm the second from the right,
The one that smiled at you tonight!
It's a hollow smile of glee
For the baldy-headed row ,
And it's just part of the show!
Life's a dance for girls like me,
But what a dance that dance can be.

REFRAIN
Dancing lady, be a soldier
You were hired for never gettin' tired
Do exactly what is told ya.
Duchess, where's that smile?
Dancing lady, dance your head off.
Keep rehearsin' and never mind the cursin'
Though your lips have bit the red off.
Duchess, where's that smile?
You have no time to sleep,
You've no time to weep,
No time for romance,
Only time for dancing.
Dancing lady, struttin' for us,
Don't let down now.
You gotta go to town now!
It's the merry, merry chorus
Duchess, where's that smile?



PATTER
Ting-a-ling, the old alarm clock's ringing
Ting-a-ling, all right, I'm out of bed.
Here's a roll. Look out you'll spill your coffee.
Hurry up and both your dogs are dead.
Hurry up. Now you've made the subway.
What a nerve! Fresh guy! Watch those...
Times Square!
Let me get through there.
Here's the theatre. Ten a.m.
Heads up!
Into your bloomers,
Just like all the rest of them!
Toe Heel Toe Kick
Toe Heel Toe Kick
Toe Heel Toe Kick
Gosh, that movement makes you sick.
One a.m.
Lunch with the rest of them.
Coffee and a bun.
Back at one.
Toe Heel Kick
Five o' clock, six o' clock,
Dinner back at eight.
Nine o' clock, ten o' clock,
Goodbye to that date!
Eleven, twelve, one,
That director's a son of a gun.
Toe Heel Kick
Kick, you bimbo, kick.

CODA

Dancing lady, struttin' for us,
Don't let down now.
You gotta go to town now!
It's the merry, merry chorus
Duchess, where's that smile? 

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