E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
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.