Arakawa under the Bridge - 1x01 - Bridge- Followmy.tv

Falling off a bridge while trying to get his pants back Ichinomiya Kou is saved by a woman named Nino. Desperate to live up to his family motto of never being indebted to anyone he tries to pay Nino off only to find that she is completely uninterested in his riches and prefers living under the bridge.
Desperate to the point of panic to be rid of his debt to her he asks if there is anything she wants. "Could you fall in love with me," she responds and so Kou ends up living under the bridge as well doing his best to fall in love with her.