I have heard that high school students, working in the local public library (which is part of the school district) on a part time basis, are exempt from Social Security and Medicare tax withholding. Is this true?

If the student is a part-time emplyee of the school he attends, then yes. So I guess the question is whether the library is considered to be a part of the school he attends. This may be tricky - if the library is not specifically aligned with the school he attends then probably not. For example, if the library's primary mission is provide library services to the general public, as opposed to library services for only the school he attends, then he may not be exempt from FICA withholding. I bet this question has come up before and the library payroll department has already made a determination about this - what do they say?

They have NO idea!

The local public library is normally NOT directly affiliated with the school board.

Hence, any income earned by local high school student would, In my opinion, be subject to FICA withholding.