You can find the police precinct of a specific area by checking the website of the local police department or city government. Many have a precinct locator that identifies the precinct when you specify an address. Websites with such locators include the NYPD, Chicago PD and the City of Phoenix.
In the NYPD website, the precinct finder asks you to identify your borough and enter an address, after which a map loads that shows your location as a red pin inside a blue boundary that marks your precinct. The Chicago PD has a district locator, which has fields for typing in your street number, street name, city and state. The City-of-Phoenix site has a police precinct locator that requires you to enter your address.
If the police department in your jurisdiction is not divided into precincts, you can find the contact information of your local police department by using PoliceLocator.com. Its home page lists all 50 states alphabetically and also shows a map of the country. Choose your state from the list or the map, and a link opens up alphabetically listing all the police departments in that state. Since they are all named after the place that they serve, such as a city or county, simply click on the one that you are interested in to get the address and telephone number.