Preferrably from urban areas. I'd be most interested in England for obvious reasons, but I'd love any that might be around. A Roman (any time, but after the 300ad decline would be fascinating) or a German one of any sort pre-20th century would be incredible as well. I know these places had police forces, but I'm unsure if they logged the crimes that were committed either by themselves or perhaps as part of a memoir. I'd also be interested in church records of heretics and their punishments from around the 12th to 17th centuries
Again, just about anything would help though, I just want to get a better idea of that side of daily life.
I love this sub so much
The assize court records from England and Wales are available from about 1159 and then the City of London records of the proceedings at the Old Bailey are available back to something like 1674.
In terms of punishment you might want to check out the Ordinary accounts. The Ordinary was like the prison Chaplin and for a number of years published the gallows speeches and brief bios of those condemned to death.
You might check out Crime in England 1550-1800 by J S Cockburn. (Although a hair later than your desired time frame)
http://www.nationalarchives.gov.uk/records/research-guides/assizes-criminal-1559-1971.htm
If you'd like something more related to the judicial system, and not just a sort of Bloody Register, Daniel Lord Smail made very interesting use of Marseille court records in The Consumption of Justice. It challenges the idea that a court system always lessens public violence, vendettas, etc. showing how feuds were carried on within the legal world, and still went on outside of it; the factions seem to have seen the courts as just another place to fight.