"I too have a book" is grammatically fine, but, as a native English speaker, I'm MUCH more likely to say "I have a book too."
I mean, the second sentence could mean "I have a book as well as something else," whereas the first sentence means "Someone else has a book, and so do I," so maybe they want to emphasize that it can only be translated the second way?
From what I understand, "I too have a book" is the more accurate answer. In English, "I have a book too" is ambiguous - it can mean "I have a book (as well as other things)" or "I (as well as other people) have a book". The given sentence has only the second of these meanings. To convey the first meaning, the "bhi" would need to be placed after "kitab".
They can be interchanged in some cases, but the difference is which word is emphasized. In the first example, "book" is emphasized: it could mean either "you have a book, and so do I," or "I have something, and also a book." For example, someone could ask, "Do you have a pen?" and you would reply, "Yes. I have a book too!"
In the second sentence, "I too have a book," the focus is on the speaker. It can only mean, "Someone else has a book, and so do I."
They could be used interchangeably, but if you want to emphasize the book, you use the first one, and if you want to emphasize that you are the person who has a book, you would use the second one.
In daily speech, though, the first one would be much more common. You'd probably see the second one in books or plays.