Which division investigates crimes involving diplomats and their staff?

The correct choice is the detective division of occurrence, as this division is specifically tasked with investigating crimes that involve diplomats and their staff. This encompasses a range of issues related to diplomatic immunity and international law, which requires specialized knowledge and understanding of the complexities involved in diplomatic cases.

Investigating such crimes often necessitates coordination with various governmental bodies, including the State Department, and involves understanding treaties and agreements that protect diplomats. The other divisions listed, while they have specific focuses—such as homicide or special victims—do not possess the specialized jurisdiction or training required to address the unique legal and diplomatic nuances associated with crimes involving members of foreign embassies. Therefore, the detective division of occurrence is uniquely suited to handle these cases, ensuring that investigations align with international protocols and standards.