Ibitsu

An urban legend in Tokyo states that at midnight, a girl dressed as a lolita will appear and ask you one question. You mustn't answer this question, however, for if you do the girl will come to be your younger sister. She will say that she has finally found her big brother, and insinuate herself into every aspect of your life... until she finally gives you a "twisted" death.

Kazuki, a young college student living in a small apartment building, is taking out his trash one night when he sees a disheveled young woman dressed in lolita-style clothing sitting in the street by the neighborhood trash pile. Unnerved, he tries to ignore her and pass by, when she asks him a single question: "Do you have a younger sister?" Surprised, he answers that he does, before running off to the safety of his apartment. Passing it off as an isolated encounter with a strange woman, Kazuki decides to think nothing more of it.

But then he starts to see her more and more, and each time her behavior and appearance seem more unusual than the last. When he learns that she's been going through his trash and has even found a way into his apartment by passing herself off as his younger sister while he's at school, he begins to fear that she may even be dangerous. After hearing the legend of the "Strange Lolita", Kazuki becomes determined that he needs to protect himself by scaring the bizarre woman away once and for all. Unfortunately, the young man has no idea of the horrors that await him...

Ibitsu is a horror Manga drawn and written by Ryou Haruka. It was released in 2009 by publisher Square Enix, and serialized in the manga magazine Young GanGan.

Tropes used in Ibitsu include:

Axe Crazy
Kneecapping: When the Strange Lolita corners Hikari and a classmate in the gym after school one night, she takes the classmate out of the picture by smashing her kneecap with a sledgehammer.
Gorn
Kill'Em All
Murder the Hypotenuse: The Lolita's solution to the fact that Kazuki already has a younger sister is to personally make sure that Hikari is taken out of Kazuki's life... permanently.
Potty Failure: Hikari pees herself when Strange Lolita eats an eyeball.
Serial Killer: Kazuki is horrified to learn, far too late of course, that he's not the first person approached in this manner. The others who became the Strange Lolita's "older brothers" were never heard from again.
Shoot the Shaggy Dog: Kazuki is dead and has been framed for the murders committed by the Strange Lolita, who lives on to continue looking for older brothers as an "urban legend".
Stalker with a Crush: The "Strange Lolita", though she seems to be seeking more of a (albeit extremely twisted) brother-sister relationship than a romantic one.
Would Hit a Girl: Kazuki. It is very, very, VERY justified.
Yandere - Guess who?