Correct, thanks for the info.
However, if I'm under the impression that martial law has been declared and the military is not immediately on the scene, do I, as a (hypothetical) public law enforcement official, still have the responsibility to secure an area until the troops arrive?
Well, I think the basic premise for martial law is that civilian law enforcement is no longer functioning. Thus, if local law enforcement has a presence and can maintain control of a situation there would be no need for martial law.