Does FERPA require parental notification of disability assessment?
Students who are over 18 or attending college (often times 17 year olds) have control of their educational records under FERPA.  The individuals with Disabilities Education Act (IDEA) is consistent with FERPA so that the student controls access to this information too.

Students can waive their FERPA rights and often do so.  Since parents are typically paying some or all of the cost of college, they can effectively force the student to waive their FERPA rights.  Many parents do this so that they can monitor their child's grades.  

Another issue is that in order to get disability accomodations a student will normally need a medical diagnosis.  Students who have reached the age of majority (18 in most states) can see a provider and get a diagnosis without parental consent or notification. By default, this is confidential under the HIPAA (the federal law on privacy of medical records.)  

However, there's also the issue of how the student could pay for this medical diagnosis.  Since there's a potential conflict of interest for the college to provide the diagnosis (because of the costs of accommodation they might want to avoid diagnosing a disability) or just because it costs money, colleges often won't provide this service to students through their clinics.  The student would have to see an outside provider. The parents' insurance might pay for this, but then the parents would know that the child was getting medical care (but not the specific medical information which still is protected under HIPAA.)