Midori Days
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Midori Days is an anime about a girl who falls in love so badly that when she dies she somehow wakes up attached to her love interest's right hand. The anime is about how these two adjust to their strange new relationship.
The title of this anime is half in Japanese and half in English. It translates to Green Days. The girl's name is Midori, and she has green hair as well.
There are far fewer masturbation jokes in this show than might be expected.