You do not need to provide your policies and handbook to a former employee unless and only if she sues you (e.g. for wrongful termination--not that this appears to be wrongful termination, but it is unfortunately almost impossible to prevent someone from filing even a weak or baseless suit and forcing you to respond to it) and, in the course of that lawsuit, uses legal process (e.g. written questions or interrogatories; a document production request; a subpoena) to get the materials.