You might tweet it if you did not believe that you'd get any results from reporting it to the police (or already did report it and got no results).

For example, when stopped at a red light on my bicycle in Brooklyn, a van intentionally (and maliciously) bumped my rear wheel from behind. The local precinct was two blocks away so I went there with the guy's license plate number. The police declined to file a report, telling me they wouldn't be able to verify who the actual driver was given only the plate number (and time, and description, and a second eye witness). If Twitter had been a thing back then I may well have tweeted about it.