The Hating Girl is a manga about a mysterious girl who has an arrow stuck in her head and a boy who tries to understand her.
(From Wikipedia)

From Zombie Scans:
Hating girl is a manga about a girl with an arrow stuck through her head named Asumi, and the boy interested in her, named Ryouji. It's full of goofy humor and silly storylines, yet the relationship aspect of it touches on real life at times, and ends up quite endearing. Check out this silly-sweet manga and laugh at the insanity that is life with a girl that has an arrow through her head.