This is the court of public opinion, the rules of evidence are different :-)
Go read the DOJ page I linked in #58
A bit over my head. I am not sure that the fact that these are computers is essential.
Let's say that they found a bomb and there was evidence that the bomb was made in the library's bathroom. Such as, they found a trash can labeled "property of...", in the dumbster outside, with residue on it.
If the police then went to the library and said, "we'd like to look at your facilities". Do you think the library should try to stop them?
Just to make it clear; If I were the librarian and the police informed me of a bomb threat in the building, I would assist in any way I could.
By the rules of this particular institution (listed above (#71 by mrsmith)), if they came an insisted a bomb maker might have used one of the chemistry books to make a bomb, I would be obligated to ask for a warrant.