According to several Aḥaronim, one is required to search every book that one studied during the year, page by page, because a crumb of ḥametz might have fallen into one of them. These authorities maintain that the objective of bedikat ḥametz is to remove every crumb of ḥametz from one’s possession (Ḥazon Ish).
However, according to those poskim who maintain that the purpose of bedikat ḥametz is to find pieces of ḥametz the size of a kezayit, clearly there is no need for such a thorough search of books, for it is inconceivable that there could be a kezayit of ḥametz between the pages of a book. In fact, even some of the stringent poskim who say that all ḥametz must be sought out maintain that one is not required to search for the sort of tiny crumbs one is liable to find in books, because even if one sees them on Pesaḥ, there is little concern that one will want to eat them.
Therefore, one should not search his books page by page, because this is overly stringent behavior that may even cause one to waste Torah-study time. This is the accepted practice.
Nevertheless, one should not put books on the dining table during Pesaḥ unless he was careful to distance them from ḥametz throughout the year. Such books might contain a crumb of ḥametz, which could fall into some food on Pesaḥ, and any amount of ḥametz on Pesaḥ is forbidden, even if it is mixed with a much greater quantity of other foodstuffs. It is permissible, though, to read such books on a table at which one does not eat.
If during the year one places such books on the dining table between meals, he must clean the table well after eating, so that no crumbs remain. Even the stringent poskim maintain that one who is careful all year long to distance his books from ḥametz, and when bringing them to the dining table is careful that no crumbs of ḥametz fall into them, is not required to search his books, because they are already considered ḥametz-free.
The status of a bookcase itself depends upon the household. If there are no children, and the adults are careful not to put any food on the bookshelves, no bedika is required. If there are children who may have placed food on a shelf, one is required to search among the books and behind them. If the bookshelf was cleaned well before Pesaḥ, a casual search is sufficient.