One of the earliest written uses of the word �fuzz' to mean �the police' was in a dictionary called 'American Tramp & Underworld Slang' published in the USA in 1931. There, it was suggested that it came from 'fuss', a name for anyone who was over-particular or hard to please, as in "Ooh, you're such a fuss!" Obviously tramps and �baddies' would see policemen in that way!
Really, therefore, if you use the word �fuzz' to mean �police', you're basically just calling them �fusspots'.
That may not be quite the hard-man image people who use the word are trying to convey!