The duties of the Sheriff are contained within the County Code, article iii, Administration & Organization, under section 300, as shown in the excerpt below and in relation to the Police Department: 304.4.
Duties of the Sheriff, Police Department and Peace Officers.
The Council shall establish as a department of the County, a Police Department to be charged with conserving the peace and enforcing the laws of the state and the ordinances of the County. The Sheriff shall have those powers and duties assigned to sheriffs by state statutes, including the powers of a peace officer, but the Sheriff shall not duplicate or perform those duties in this charter or by ordinance or resolution assigned or delegated to the County's Police Department.