Green’s Dictionary of Slang

1. drunk and disorderly.

1914		G.D. Chase ‘Navy Sl.’ in DN IV: ii 150: D. and D. For drunk and dirty.
1931		A. Hardin ‘Volstead English’ in AS VII:2 88: Terms referring to the state of intoxication: [...] Adjectives, etc: D. & D.
1933		‘William Juniper’ True Drunkard’s Delight 247: D. and D., Drunk and disorderly.
1947		J.L. Riordan ‘Some “G.I. Alphabet Soup”’ in AS XXII:2 Apr. 109: The naval designations D and D (drunk and disorderly) and C and S (clean and sober) also antedate the war.
1949		N. Algren Man with the Golden Arm 127: D. ’n D. don’t mean ‘drunk ’n disorderly’ in my case [...] it means Damen ’n Division.
1956		‘Charles Raven’ Und. Nights 22: In comes a bright bogey who knows who she is and nicks her on the spot for being d and d.

2. deaf and dumb.

1937		‘Boxcar Bertha’ Sister of the Road (1975) 301: Beggars [...] may be further sub-divided into groups: a. Blinkey (blind) b. Deafey (deaf) c. Dummy (dumb) d. D & D (deaf and dumb) e. Army or wingey (armless) f. Peggy (legless) g. Crippy (paralyzed) h. Fritzy (epileptic) i. Nuts (feeble-minded or insane) j. Shaky (with pronounced tremors).
1955		B. Schulberg On the Waterfront (1964) 155: On the docks we’ve always been D ’n D [...] Deef [sic] ’n dumb.
1969		Time 21 Mar. 21: Playing D. & D. (deaf and dumb) with cops was a lesson taught in the quiet back rooms of precinct houses.
1972		E. Grogan Ringolevio 154: The questioning went on and on with Kenny playing D & D.