Green’s Dictionary of Slang

Arizona n.

[see cit. 1946]

(US short order) buttermilk.

R. Shafer ‘The Lang. of W. Coast Culinary Workers’ in AS 87/2: Arizona – buttermilk (because a waitress thinks any man drinking buttermilk [rather than liquor] ought to be in Arizona for his health.
[US] Wentworth & Flexner DAS 8/1: Arizona n. Buttermilk.