This is certainly a strange game; its source is the form-changing rhyme of the witch. Margaret Murray refers to it in The Witch-Cult in Western Europe and in The God of the Witches. Isobel Gowdie of Auldearne, burnt as a witch in 1662, gave the formula for the transformation to a hare as follows:

I sall goe intill ane haire
With sorrow, and sych and meikle caire;
And I sall goe in the Divellis nam
Ay quill I com hom againe.
(I shall go into a hare
With sorrow and sighing and mickle care;
And I shall go in the Devil's name
Aye, till I come home again.)

for a cat:

I sall goe intill ane catt
With sorrow, and sych and a blak shot...

and for a crow:

I sall goe intill a craw
With sorrow, and sych, and a blak thraw.
(Murray, Witch-Cult, p. 166)