Public libraries offer many services for their patrons. I will use the East Lansing Public Library as an example.
Public libraries offer a wide range of material in print and even in ebook and audiobook format. While the collections of public library's are not as research intensive as a university library, Public libraries often participate in InterLibrary Loan. For example, East Lansing Public Library participates in MelCat.
Public Libraries also provide access to a selection of electronic databases. For example, click here for the databases offered by the East Lansing Public Library.
Many State Universities provide access to some of their resources for patrons that live in the state in which the university is located!
Michigan State University as a Land Grant Institution makes a committed effort to make resources available to the wider community. Land Grant Universities and Public Universities have policies and procedures for community borrowers similar to Michigan State University.