Green’s Dictionary of Slang

a nickname for a bald person.

1953		S. Bellow Augie March (1996) 426: He said to some bald-headed guy, ‘Push over, Curly!’.
1984		Partridge DSUE (8th edn) 280/1: since ca. 1910.
2000		Hartford Courant (CT) sect. D 5 Sept. 27/4: G’Day from Down Under [...] Curly — a bald person.