An illustrated copy at the Bodleian has the chorus:
To my high ho, the carrion crow, sung croak, croak,
       croak, fol de rol &c.
Harding B 12(10), printed by J. Pitts (London), between 1802 and 1819.
Another copy at the Bodleian printed by Watts has a different chorus:
Caw, caw, the carrion crow,
Dig, dig, in the ground below.

The version in Opies, Oxford Nursery Rhyme Book, has the better known chorus:
Sing heigh ho, the carrion crow,
Fol de riddle, lol de riddle, hi ding do.