Your question is rather vague, but I will try to answer, at least for medieval times.
In this period, the police were not the only people who had to look after the public peace. In common law, a hue and cry was the act of screaming out that a crime had been committed, for example: "Thief!" When the cry was heard, all able bodied men had to stop what they were doing immediately and chase down the accused. They would later be tried.
This hue and cry was used for everything illegal. If you found a body, you would cry out. The purpose was to alert the people in the area to look out and catch the accused before they fled and bring them to justice. However, if one were to use a hue and cry without proper cause, such as crying murder for no reason, you could be tried and punished as well.
This is not to say that there was no police system in medieval times, as it rather relied on the area and whether or not a lord allowed his soldiers to be used as police or whether he would pay others to do it.
They ran down the street to...
Find the cop on the beat walking around.
The nearest substation or police box.