And no one seemed to mind that the models had a bit of fuzz on their legs—or that none of them wore any pants.
1590s, fusse, first attested in fusball "puff ball of tiny spores," of uncertain origin. Meaning "the police" is American English, 1929, underworld slang, origin and connection to the older word unknown. Perhaps a variant of fuss, with a notion of "hard to please."
A police officer; the police: Cops must be annihilated. Kill the Fascist fuzz
[1930+; origin unknown; the form fuzey is found at about the same time]