Green’s Dictionary of Slang

(US) the vagina.

c.1927		in P. Smith Letter from My Father (1978) 190: She had been showing herself, her tits and cuzzie to the driver whenever he stopped at the traffic light and could look.
c.1930		in P. Smith Letter from My Father (1978) 240: That most heavenly shrine of all mankind, her cuzzy.
1930		(con. 1917) ‘W.W. Windstaff’ ‘A Flier’s War’ in Longstreet Canvas Falcons (1970) 275: ‘Envy you the cossie in Arras.’ He made an obscene thumb jabbing gesture.
1938		J. Weidman I Can Get It For You Wholesale 3: What’s more important than cuzzy?
1966		Trimble 5000 Adult Sex Words and Phrases.