Urusei Yatsura: Only You (1983)

When everyone in town receives invitations to Ataru's wedding, they are shocked to see that his sweetheart Lum is not the bride. Eventually they learn that when Ataru was playing games as a little boy, he stepped on a girl's shadow. Unbeknownst to him, the girl was from extraterrestrial culture where stepping on one's shadow is a form of marriage proposal, and now she and her family have come back to see that Ataru keeps his promise. If he manages to get out of this without being killed by her folks, he'll still have to avoid being torn apart by the hands of Lum.