Yuuyami to Kataware

"I'm a vampire."

"Give me your blood, mister."

A man about to throw himself off a bridge is suddenly stopped by a vampire girl—one who looks just like any other ordinary high school student. He decides he wouldn't mind dying if it's at the hands of such a beautiful girl; however, instead of death, an unexpected bond begins to form between them. A series of tales where humans and the uncanny meet—lost halves finding their echo.

(Source: Kodansha)