It depends on what you are studying about the book. As a different example: if you study a painting, you not only examine all the aspects of the image portrayed but possibly also the brushwork, the framing, the presentation, and other elements.
In the same way, if you study a book, you might examine the binding, the print, the paper, the cover, and all the other elements that make up a book.
(As a side note, this particular academic field is called Philology. A philologist will study not only the text of any written document, but all the materials of its construction, as well as the cultural and historical factors that may have influenced its publication.)
On the other hand, if you are instead reading the text of a book in order to learn its contents (such as for school), then you are correct, and study from a book sounds more appropriate.
That being said, I would not use any of these. I study some material for some purpose, e.g.
I'm going to the library to study chemistry for my midterm exam next week.
Otherwise I would simply read, or learn from something like a textbook, not study it.