Originally: the headquarters of the police force in a city or town. Now: an office dealing with enquiries, reports of minor crimes, and other non-urgent police business.
In Britain the police office originally included a courtroom in which offenders were tried, as well as a place of detention in which they were confined until trial; hence the name was formerly regularly applied to what is now called a police court.
Late 18th century; earliest use found in India Gazette. From police + office.