I hardly remember any of it, but I recall right near the start there was an attack by a huge monster. It looked a bit like a long-haired Afghan hound or something, almost nothing but hair, and as I recall it then revealed that it'd stolen the hair (and I'm pretty sure heads) of the girls it'd killed.

I don't think it's the same series though it might be, but I also recall a story where a girl ends up being sent to some sort of yokai school or something, where everyone else is either a yokai or a beastperson or something, and she's the only human. I recall the girl's name was Neko, and as a result I think at least some people thought she was a cat girl or something.