It is a bit ambiguous in this case.
The anime finished after the manga:
Anime finished: April 02, 2010
Manga finished: January 22, 2010
... But we could not confirm the source content in MangaUpdates.
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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In a unique world, people transform into books after death, their lives becoming readable narratives stored within the vast Bantorra Library.
This library is protected by the Armed Librarians, individuals with extraordinary psychic abilities, tasked with preserving and defending these invaluable records of human existence.
However, the Bantorra Library and its librarians face a formidable adversary: the Sindeki Kyoudan, a powerful religious organization with motivations that directly conflict with the library's purpose and the preservation of individual histories.
The anime revolves around the struggles of the Armed Librarians as they navigate complex political landscapes, confront the dangerous Sindeki Kyoudan, and grapple with the ethical dilemmas inherent in possessing the power to read and share the lives of the deceased.