Actually America's first police department started in Boston in 1838 and, while it wasnt formalized until 1854, New York, New Orleans, and Cincinnati all had formal departments by the time that it was.

While more can always be written on this topic...This answer of mine deals with origins of police departments and slave patrols in America, and this one deals with how laws were enforced before police departments were formed.

Let me know if those don't cover what you're looking for.