There is no mention of the exact contents of the notebook in the original VN or the anime. There are a couple of short sequel games which I have not gone through, so in principle there could be some explanation there, but given how important this is I doubt they'd want to relegate it to a side-game. Hence, the authors have definitely and deliberately hidden what is in her notebook.
However, there are some good theories. The most common viewpoint is that she was using the notebook as a diary to vent her frustration with everyone else, particularly her sister. Despite the fact that Tsukasa is harder-working, her sister always seems to be more popular. Of course, she has more to vent about than that, and it's pretty safe to guess that the diary contained all sorts of things about everyone. That's why, if it ever went public, she wouldn't be able to go to school any more.
This forum post provides a pretty complete and fairly consistent picture of Ayatsuji from a psychological standpoint. The segment about her notebook is quoted below:
The Birth and the Function of her Diary
We believe that [having someone/something to listen to her] was the function of her diary, which she so desperately guarded. Here, the Inner Tsukasa was writing down her life, her frustrations, and her thoughts which she couldn't share with anybody. In a way, it was her way to deal with whatever gave her a hard time. Some kind of offline-blog, talking to herself. It also explains why the contents would be damaging enough that she "couldn't come to school anymore" if they'd ever come out.
We could see in episode 3 how much she was annoyed at the laziness and pettiness of the three bitches. Her Facade would have never allowed to show her anger - instead, it rather demanded that she would go through a humiliating insincere teary apology, sacrificing her (absolutely justified) anger and pride for the sake of ultimate success. In the past, she probably would have made an entry in the diary - this time, she did it in person, with disastrous results.
This is how Junichi uncovered the "Inner" Tsukasa - when he picked up the diary. Tsukasa believed that he had actually read it, and that there was no need to maintain the Facade towards him anymore. It also proves that Ayatsuji has no split or bipolar personality: The Inner Tsukasa is always in control - she was able to drop the Facade in a second.