Citations to print materials generally do not include the facility in which the book was located. Not including the library’s name is considered proper form–after all the same book can be in more than one location.
Like every rule, there are exceptions. Those exceptions are usually when there is something about the printed book that makes it different from other copies of the same printed book.
The book, Sargent genealogy: Hugh Sargent, of Courteenhall, Northamptonshire and his descendants in England, was written by Aaron Sargent and published in Somerville, Massachusetts, in 1895.
The copy of this book at the Allen County Public Library in Ft. Wayne, Indiana, is a little different. It has personal note written by the author. If I want to reference the note, my citation for this book needs to indicate that it is at the Allen County Public Library. That’s the only library whose book has this inscription.
At least I’m assuming that to be the case. The digital image of the book (available at Google Books was made from a copy of the Historical Society of Wisconsin and does not include such an inscription).
There are times when one cites a specific copy of a book in a specific library–but that’s if that library’s copy has something in it that makes it unique–almost making the book a published book that contains an unpublished manuscript.