What department is responsible for arrests and investigations within the district?

The correct choice indicates that the Sheriff - Coroner's department is responsible for arrests and investigations within the district. The Sheriff's department typically plays a critical role in law enforcement at the county level, which includes managing investigations, conducting arrests, and providing overall public safety services.

The Sheriff’s office often handles more than just crime response; they are involved in community policing, traffic enforcement, and the management of county jails, all of which necessitate a capacity for investigation and apprehension of suspects. Their jurisdiction is much broader than that of local police departments, allowing them to operate throughout the entire county.

In contrast, the other options refer to entities with more localized or specific functions. For instance, Brea Police and Anaheim Police primarily focus on law enforcement within their respective city limits, while the District Attorney is responsible for prosecuting criminal cases but does not engage directly in arrests or investigative procedures. Thus, the Sheriff - Coroner's department is aptly situated as the entity with the appropriate jurisdiction and resources for conducting arrests and investigations throughout the district.