From Outdoors magazine:
Crazy as a March Hare
Hares have an interesting place in the English language.
Have you ever heard the phrase "Mad as a March hare" and wondered where it came from?
March is the breeding season for hares, thus their odd behavior of boxing and jumping during this time of year. This is not a new phenomenon, and the earliest written testament to it was circa 1500, in Blowbol's Test reprinted by W. C. Hazlitt in Remains Early Popular Poetry of England, 1864. It states, "Thanne [th]ey begyn to swere and to stare, And be as braynles as a Marshe hare."
In hunting circles, the phrase derived from a male hare's (bucks) tendency to travel several miles to breed with a female (doe) during the month of March. When a hunter's dog would disturb the buck, he would return to his home area miles away with the dog often in pursuit. This meant the hunters would either lose their dog or have to travel miles to find it.
The phrase "hare-brained" refers to the same behavior. This is also old and is referenced in Edward Hall's Chronicle, 1548: "My desire is that none of you be so unadvised or harebrained [sic] as to be the occasion that ..."
Other interesting facts about hares include that the rabbit in Bambi named Thumper derived its name from a female hares’ tendencies with her young. Hares do not live in the ground like cottontails, so they have their young above ground and the babies (leverets) spread out to hide so that if one is discovered by a predator it will not find the entire clutch. When it is time for the young to nurse, the mother hare will "thump" her back foot rapidly to call them in to feed.