I don't know about Athens, but I answered a similar question a few months ago about your chances of being caught if you murdered someone in Rome - in brief, the Romans felt that murder was an issue between private citizens, and not something for the government to get involved in. There wasn't really a concept of a "state" yet so there was no state to investigate crimes. The murdered person's family would have to bring an accusation against someone specific, then the court could investigate - if the dead person had no family, or if they didn't know who to accuse, there wouldn't be anything to investigate.