Ypsilanti District Library does have a very nice system, which is not part of the City, (it's a separate, pseudo-governmental entity) but does offer library cards for free to any city resident. Most "public" libraries are similar

But I'm talking about Eastern Michigan University's library here. In my experience, it's rare for a university library to be so free with library cards. At University of Michigan, you can use the library without an active UMich affiliation, but you can't (to my knowledge) check books out. When I lived in Princeton, NJ, I couldn't even get in the door of the Princeton University library as a non-student - the guards at the door demanded University ID, and would actually check to see if you were the person pictured on the ID.

Maybe freer library rights are common at less stuck-up universities than UMich and Princeton. My opinion, though, is that for a library the caliber of EMU's Halle Library, the openness and accessibility is pretty admirable.