The Star and Crescent badge, unique to the NOPD, has been worn by members of the department since 1855. The crescent represents the shape of the city, as the Mississippi River forms a crescent shape around the city.The star represents the power of a state or local government to preserve order and keep the peace; it is a traditional symbol of law enforcement authority in the United States.
http://en.wikipedia.org/wiki/New_Orleans_Police_Department