I don't think SS uniform skull is in any way related to similar insignia in other nations, as suggested by @TheHonRose. I believe it was introduced by Hugo Boss circa 1933 when he designed Nazi uniforms, and the meaning of it was something like "Loyal until death". I don't recall the reference though; you may want to look into early history of Hugo Boss fashion house.
Now, as to where Hugo Boss got the idea of putting a skull on SS uniforms - that I don't know; Oldcat's conjecture about Totenkopf sounds very plausible.