The APD started as "city watchmen" with the granting of the city charter in 1708. At the time, the Anne Arundel County Sheriff's Office held concurrent jurisdiction within Annapolis proper for the first six years, after which the city would elect its own Sheriff (as is the case still today in Baltimore).
The term "police officer" was not used until 1861. Like today, these police officers answered to the mayor of the city. It wasn't until 1867 that the Annapolis Police Department was officially created by an act of legislation by the Maryland General Assembly. 
The current chief of police is Joseph S. Johnson and has been the sitting chief since 1994. The APD has an authorized strength of 126 sworn officers, 52 full-time civilian support staff, and 32 part-time support staff. The department also employs within its sworn ranks 16 certified bicycle officers, 3 specially trained canine (K-9) officers, and 3 certified D.A.R.E. officers. The budget for the APD was $14.5M (FY06).