Most public libraries allow access to computers by non card holders. They will give you a temporary passcode, usually with a time limit on use. I have accessed the internet at public libraries where I don't have a card because I live elsewhere.
If evidence was found, the challenge would be linking the code to a specific user since the library will have no personally identifying info on record due to privacy laws. Library use records can be obtained by LE. However, once again due to privacy laws and a commitment to upholding them as promulgated by the American Library Association (backed by the U.S. Constitution), it is very unusual but not unprecedented to release any user information without a legal document demanding it.
Having obtained a master's in library science and work experience in county library systems, I am familiar with the usual privacy protections they have in place.
IMO