A hare-brained person who scares quiet folk. Some derive it from the French clameur de Haro (hue and cry), as if the madcap was one against whom the hue-and-cry is raised; but probably it is simply a jingle word having allusion to the “madness of a March hare, ” and the “scaring” of honest folks from their proprieties.
“Who's there? I s'pose young harum-scarum.”
Cambridge Facetiæ Collegian and Porter