The Idea Factory - Menace and Angel
The book starts out introducing a character and solidifying that she has an identical twin out there somewhere. When they were supposed to meet up, though, the twin doesn't show up. She starts worrying about her, looking for her and reporting her missing. Over the course of the book, though, there are no signs of the sister. At some point, she goes to her shrink, and the shrink reminds her that she doesn't have a sister. She has disassociative identity disorder and the twin is her alternate personality.