For questions about maintaining library access, always consult the Graduate School's resources or your department's resources first.
For PhD students completing their dissertation and needing continued access to the library, you will likely need to enroll in one of the following courses:
• Doctoral Candidate Status I-IV: Dissertation Research and Direction (courses numbered 9991-9994 in each department),
or
• Candidate Maintenance Status: Doctoral Dissertation Research and Direction (course number 9995 in each department).
An overview of all of the forms for PhD students can be found at this link, as well as other PhD student information. Again, your best bet for up-to-date information on library access as a graduate student is still the Graduate School, however.