Green’s Dictionary of Slang

(US police/Und.) of police interrogators, to take the parts of the ‘good/sympathetic’ and ‘bad/potentially violent’ officers when attempting to gain information from a suspect. Such ‘roles’ are assumed only for the situation in hand.

1980		G. Liddy Will 204: Hunt and I arranged to meet him in Florida where we’d ‘Mutt and Jeff’ him (the old good cop, bad cop routine).
1981		R.O. Butler Alleys of Eden (1991) 38: I’ll play it tough. You’ll be the good guy. We’ll Mutt and Jeff him. You know the routine.