For the 2010 film, see The Precinct. A precinct is a space enclosed by the walls or other boundaries of a particular place or building, or by an arbitrary and imaginary line drawn around it.The term is often used to refer to a division of a police department in a large city (either to the neighborhood patrolled or to the police station itself).ach precinct has a specific location where its residents go to vote. Sometimes several precincts will use the same polling station. A 2004 survey by the United States Election Assistance Commission reported an average precinct size in the United States of approximately 1,100 registered voters.