Green’s Dictionary of Slang

slim n.2

[? their attempts to be unobtrusive; but note slim adj.]

1. an informer.

[US]M.C. Sharpe Chicago May (1929) 259: Slims, Rats, Squealers, Squawkers, Stool-Pigeons, Stools, Pigeons or Narks (English)—police informers.
[US]Howsley Argot: Dict. of Und. Sl.

2. (US prison) a police spy.

[US]San Quentin Bulletin in L.A. Times 6 May 7: SLIM, a police spy.
[US]Howsley Argot: Dict. of Und. Sl.
[US]Monteleone Criminal Sl. (rev. edn).