From Harry's Blues Lyrics Online, Arthur Big Boy Crudup Lyrics, page 1.

THAT'S ALL RIGHT (MAMA)

by Arthur "Big Boy" Crudup
recording of 1946-1949
from That's Allright Mama (Relic 7036) & That's Allright Mama (RCA 61043-2 or Black Label 2006) & The Father of Rock & Roll (RCA LPV-573) & Look on Yonder's Wall (Delmark 614) & Complete Recorded Works, Vol. 2 (1946-1949) (Document 5202), copyright notice

Well now, that's all right now, mama. That's all right for you.
That's all right, mama, just any way you do.
Now that's all right. That's all right.
That's all right now, mama, any way you do.

[Missing verse]

Well, my mama she done told me. Pap's done told me too:
"Son, that gal you're foolin' with, she ain't no good for you."
But that's all right. That's all right.
That's all right now, mama, any way you do.

I'm leaving town tomorrow, leaving town for sure.
Then you won't be bothered with me hanging 'round your door;
But that's all right. That's all right.
That's all right, mama, any way you do.

I oughta mind my pap. Guess I'm not too smart.
If I was, I'd leave you, go before you break my heart;
But that's all right. That's all right.
That's all right, mama, any way you do.