Seems close to....

DON'T YOU GRIEVE AFTER ME

I went to the river an' I couldn't git across
I paid five dollars for a old stable horse
I plunged him in an' his rump caved in
An' I told him not to grieve after me

When I'm gone, don't you, don't you grieve (3x)
An' I told him not to grieve after me.

I went down town a-feelin' funny
Picked up a pocketbook chuck full of money
Police come along, says "Drop that, sonny!"
An' I told him not to grieve after me.

I went to the hotel to stay all night
He says, "Fifty cents," an' I says "All right."
I jumped in bed an' covered up my head,
An' told him not to grieve after me.

Got up next mornin' an' washed my feet
Went down to the table an' you orter seen me eat;
Jumped up quick an' hollered, "Dead beat!"
An' told him not grieve after me.

Randolph/Cohen, Ozark Folksongs, p.220-222.

Randolph and Cohen both say it is related to African-American spirituals.

And here's what the Ballad Index has to say...

Don't You Grieve After Me (I)
DESCRIPTION: The singer describes various adventures: Being found by the police with a wallet not his own, sleeping in a hotel and being declared a deadbeat. Chorus: When I'm gone, Don't you, don't you grieve (x3), An' I told him not to grieve after me."
AUTHOR: unknown
EARLIEST DATE: 1915
KEYWORDS: rambling crime travel floatingverses
FOUND IN: US(So)
REFERENCES (3 citations):
Randolph 257, "Don't You Grieve After Me" (1 text, 1 tune)
Randolph/Cohen, pp. 220-222, "Don't You Grieve After Me" (1 text, 1 tune -- Randolph's 257)
BrownIII 556, "Bye and Bye" (1 fragment, possibly not this but too short to classify as anything else)
Roud #6698
RECORDINGS:
Loman D. Cansler, "I Told 'em Not to Grieve After Me" (on Cansler1)
CROSS-REFERENCES:
cf. "Don't You Weep After Me" (floating lyrics)
ALTERNATE TITLES:
I Told Him Not to Grieve After Me
Notes: Alan Lomax claims -- on the basis of a few words in the chorus -- that this is the same as "When I'm Gone." I don't buy it. - RBW
File: R257