The handgun being used by the killer is a Magnum Research Desert Eagle. It is most likely chambered in 357 Magnum, 44 Magnum, or 50 Action Express (AE).
At one point the veteran detective refers to the victim as an "NHI". In the 1980s, police in LA used to refer to the murders of prostitutes, gang members, and drug addicts as NHI, "No Humans Involved."