Green’s Dictionary of Slang

(US) a police patrol car.

1927		‘Jargon of the Und.’ in DN V 449: Handy wagon, The police patrol wagon.
1931		Irwin Amer. Tramp and Und. Sl. 95: Handy Wagon. – A police patrol; always handy for use when needed.
1939		Chicago Trib. 22 Jan. 9: Handy Wagon—A police wagon [HDAS].