Urusei Yatsura '87: Inaba the Dreammaker

It is summertime, and Shinobu laments not having a boyfriend. She then happens upon a young man weak from hunger, and wearing a rabbit costume. She gives him a carrot, he expresses his gratitude by hitting on her... and she hits back. The young man leaves behind a key to another dimension where everybody's possible futures exist. Lum and Ataru join Shinobu to find the bunny boy, and happy futures for themselves. (imdb)