I run a book / tape gemach. If people. hold my books over Pesach who is responsible that it be clean of chametz? I as the owner or the person in whose possesion it is over yom tov?
In a different post, we have clarified that according to many authorities, there is no full obligation on checking books on Pesach. According to authorities who state there is an obligation, it would fall on the person who has possession of the books over Yom Tov.
For the question of checking books, see here.
Concerning the principle question of checking, the obligation falls on the person in whose possession the book (or other item) will be over Pesach. One who borrows something from a gemach has the status of a shoel, and the item entirely enters the borrower’s domain, obligating him in checking for chametz.