Urusei Yatsura: STAY WITH YOU

Urusei Yatsura: Stay with You is based on the manga series by Rumiko Takahashi. The protagonist is Ataru Moroboshi, a high school student who accidentally evokes love in the heart of Lum, the princess of an alien demon-like race. The game does not recount the initial events of the manga and instead is built like an episode, assuming the player's familiarity with the general story and characters. Ataru's ex-girlfriend Shinobu disappears under mysterious circumstances. Ataru and Lum must explore the high school building and find out what happened to Shinobu.

[From mobygames]