Green’s Dictionary of Slang

1. to steal from.

1906		A.H. Lewis Confessions of a Detective 50: Not a dollar! And every month, mind you, you ought to be coppin’ off at least two hundred plunks.
1921		P. & T. Casey Gay-cat 160: It’ll be a cinch fer him ter cop off this place.
1932		E.S. Gardner ‘Bird in the Hand’ in Goulart (1967) 272: He’s got the hiding place of those diamonds figured out, and he’s going there to cop ’em off.

2. (US) to arrest.

1921

P. & T. Casey Gay-cat 234: Mostly we has ter cop off the strong-armers an’ stick-ups an’ grifters an’ dips an’ other ringtails wot pester a circus.