The Los Angeles County Sheriff has been providing air rescue services since the 1950's and has had paramedic deputies since the early 1970's. I'm going to include a link to the LASD website that describes the program and has pictures of some of the aircraft and equipment they use.
As for the closest sheriff station to Carson...the city where station 51 was located...I know that there was, and still is, a sheriff station in Carson, I just don't know how far away from the fire station it is.
Here is the link I mentioned.
www.lasd.org/sites/stn-aero/air5/tradition.htm