National Information System for Health Related Services Act of 1987 - Amends the Developmental Disabilities Assistance and Bill of Rights Act to direct the Secretary of Health and Human Services to make grants to an academic institution for the operation of a National Information System for Health Related Services. Requires such system to: (1) provide information and referrals regarding services available from public and private entities for persons with developmental disabilities or chronic illnesses and their families; (2) use a central computer system accessible to the public through a toll-free telephone number; (3) train people who will receive and answer requests for information and referrals; and (4) conduct periodic followup on referrals. Allows payments under the grants to be in advance or by way of reimbursement.

Authorizes appropriations for FY 1988 through 1992.