Back in the early 1970s I got to know Hamish Imlach somewhat as he spent some time doing a number of shows in the town where I lived - I think I attended all of them. He was a real character and a great folksinger. And as Susanne (skw) on 03 Sep 01 (above) notes, this song was in his repertoire.
It's good to know Leadbelly's original version and I respect it for what it is. However, I prefer Hamish's version. The lyrics as I hear them are:

Jean Harlow died the other day
And these are the last words I heard her say
Yes, Jean Harlow died the other day
And these are the last words I heard her say

Refrain:
Tingalinga tingalinga ba da ba doo ba da ba,
Tingalinga tingalinga ba da ba doo ba da ba,
Tingalinga tingalinga ba da ba doo ba da ba day, and
Her mama's gonna walk, and mama talk,
Her mama's gonna walk, and mama talk,
Her mama's gonna walk, and mama talk, in New York

Well, her mama come in, she was lookin' mighty wild
She said, "Doctor, doctor, please save my child"
Yes, her mama come in, she was lookin' mighty wild
She said, "Doctor, doctor, please save my child" and...

And the doctor come in, he was lookin' mighty sad
He said, "This is the worst case I ever have had"
Yes, the doctor come in, he was lookin' mighty sad
He said, "This is the worst case I ever have had"

Well just before Jean Harlow died
She said "There's just one more movie picture I'd like to ride"
Yes, just before Jean Harlow died
She said "There's just one more movie picture I'd like to ride" and...


This Hamish Imlach version can be heard at this website:
http://topmp3lyrics.com/lyrics/Jean-Harlow-Died-The-Other-Day-Several-Times/6997895
Note: the added noises at the beginning does not extend through the song.

Here's where you can hear Leadbelly's version:
http://www.youtube.com/watch?v=OufFJiFgYrI

Added note:
CRUDITY WARNING:
To add to the point from Susanne, Hamish could get pretty ribald in his live shows, especially in bars, and when I saw him back then, he sang the last verse using "There's one more movie star I'd like to ride" ending with "- Trigger"