All three are sent for most vehicular accidents for traffic control (state police, county sheriff, or city), fire suppression (volunteer FD, usually), and medical services (sometimes volunteer, especially in the county). Judging by the comments below, I suspect there's an advantage to living in an area that doesn't have tax money to blow. ;)
This nation would have much better policing if we had half as many cops. I had a single day of jury duty two weeks ago and was dumbfounded by how many sheriff's deputies there were wandering around the courthouse in a daze, loitering around the metal detector, setting off the metal detector, speaking at inappropriate volume, eating in unsettling fashion, etc.
But hey, Australia is surprisingly progressive in this way: I just got my prescription for Naloxone needles and did my training today. I'm an ex-addict, and don't hang with those people very often, but if I ever do I can save an overdose :) this is in QLD of all places, despite Newman trying to turn us into a police state.