Damage to a Book in a Synagogue

I accidentally tore a page of a book in a synagogue. Do I need to inform those responsible for the synagogue?

Shalom!
I did not fully understand the question.
If the question pertains to the payment for the damage, any damage that occurs due to reasonable use is exempt. This is derived from the law of a person who borrowed a work animal and the animal died as a result reasonable use. The borrower is exempt from payment in this case.
If the question is whether one should inform the person responsible for synagogue’s library, so he’ll be able to repair the book for the benefit of the public, it is appropriate and worthwhile to do this.