The last of the four "Bugs goes to outer space" shorts, following Haredevil Hare (1948), The Hasty Hare (1952), and Hare-Way to the Stars (1958). It's also the last appearance of Marvin the Martian in the original theatrical shorts until Marvin the Martian in the Third Dimension (1996), though the character would later re-appear in Spaced Out Bunny (1980) and Duck Dodgers and the Return of the 24 1/2th Century.
The title refers to as "mad as a March hare" a idiomatic phrase derived from the observed antics, said to occur only in the March breeding season of the Hare, genus Lepus. In Alice In Wonderland one of the characters in a March Hare.
Marvin Martian breaks the fourth wall in this short as he addresses the audience. He once again sports hi top sneakers and a centurion costume, complete with broom like helmet topper.
The Acme products catalog reaches Mars, given the label on Marvin's weapon.
Marvin Martian's head is viewed in this short, just for a moment. It appears to be a perfectly round black sphere, with two wide eyes and nothing else visible, due to Marvin's headgear.