When I was an undergraduate at Caltech (Pasadena, CA, mid 1950s), there was a mathematician there who walked the streets at night while ruminating on his problems. Sometimes his random walks took him to the neighboring town of San Marino, a posh municipality in which a pedestrian in the wee hours of the morning naturally excited suspicion, and he was continually harassed by the police. At length, the chief of police gave him a letter to show that said, in suitably dignified language: The bearer is a harmless nut from Caltech; no need to bother him.

A little later I heard about a student (at Reed College, Portland, OR, IIRC) who was picked up by the police for leaning against a lamppost at night, reading a book. The next night, hundreds of lampposts in the vicinity of the campus were similarly occupied.

As police states go, one could do worse than mine.