No, you don't. You won't see course work in Anthropology as a requirement for crime scene investigator jobs.
When anthropology becomes important is in cases such as unidentified remains. In those cases a Forensic Anthropologist is usually called in by the Coroner's Office to assist.
But some people do take anthropology to have a background in the subject. The CSI Certificate program at the University of California requires students to take some electives. Field Methods of Forensic Anthropology: Search and Recovery of Human Remains is one of the electives offered.
Do you need anthropology to become a crime scene investigator?