The Wisdom of Crocodiles (2000)

Handsome, witty, successful Steve Griscz has a special way with women: he seduces them quickly by winning their trust. This is more than just a game for Steve; he can't live without these women, literally, because he's a vampire and requires their blood for sustenance. When the body of his latest conquest turns up, Steve decides to get involved in the investigation before the trail leads back to him. By the time the chief detectives start their inquiries, Steve has already moved on to his next victim. He meets his match in Anne Levels, an intelligent, moody, and exceptionally beautiful woman. She doesn't reveal much about herself, so Steve can't rely on his usual psychological tricks. He needs proof of her absolute love to ensure his survival, and her refusal to display any emotion is slowly killing him.