For comparison, masato's link above gives these words from 1851 (attribution: anon). The tune on the midi is altogether more ponderous than Crumit's light, fast-moving version. And while there are similarities, I don't think the melodies are the same.

"Nancy Till" (1851)
Written for and Sung by White's Serenaders.

[Source: pages 88-89 of
"Minstrel Songs, Old and New" (1883)]

1.
Down in the canebrake close by the mill,
There liv'd a yellow girl, her name was Nancy Till;
She knew that I lov'd her, she knew it long,
I'm going to serenade her and I'll sing this song.

CHORUS
Come, love, come, the boat lies low,
She lies high and dry on the Ohio;
Come, love, come, won't you go along with me?
I'll take you down to Tennessee.

2.
Open the window, love, O do,
And listen to the music I'm playing for you,
The whisp'rings of love, so soft and so low,
Harmonise my voice with the old banjo.

(CHORUS)

3.
Softly the casement begins for to rise--
The stars are a shining above the skies;
The moon is declining behind yonder hill
Reflecting uts rays on you, my Nancy Till.

(CHORUS)

4.
Farewell love, I must now away,
I've a long way to travel before the break of day,
But the next time I come, be ready to go,
A sailing on the banks of the Ohio.

(CHORUS)