Green’s Dictionary of Slang

(US) to act in a cautious or secretive manner; thus cozy adj., sly, cunning.

[1924		L.A. Eve. Exp. 16 June 12/2: Laura Jean Libbey played it cozy by staying at home].
1929		C. Coe Hooch! 62: I don’t blame you for playin’ the game cozy.
1936		Monks & Finklehoffe Brother Rat I i: Why is she down here on Harrington’s bid? Think she’s playing me cozy?
1957		(con. 1943) A. Myrer Big War 102: Well you haven’t done so brilliantly [...] for all your cozy-dog sucking around.
1967		R. Starnes Requiem in Utopia 165: ‘With the Pentagon people here it might’ve been wise to play it real cozy.’ ‘Lie doggo, so to speak?’.
1973		L. Shecter On the Pad 256: He felt [...] that eventually Finelli would be paying off top brass, and all the commission had to do was play it cozy.
2000		Lehr & O’Neill Black Mass 258: Krantz played it cozy, but he was intrigued by the idea that he could stay out of jail and get some of his money back if he did a little talking.