Green’s Dictionary of Slang

felony hat n.

(US police) a broad-brimmed hat of a sort stereotypically worn by pimps.

[US]B. McCarthy Vice Cop 166: Smith also lived out the stereotype of the Super Fly, sporting capes and what the Vice cops referred to as ‘felony hats’—wide-brimmed, garish fedoras in the early 1970s.