Social Security Act Mental Health Amendments of 1987 - Amends titles XVI (Supplemental Security Income) (SSI), XVIII (Medicare), and XIX (Medicaid) of the Social Security Act to provide benefits for chronically mentally ill individuals.

Requires State plans under title XIX to include case management services and home and community-based services for such individuals. Directs the Secretary of Health and Human Services to arrange for up to five States to conduct demonstration projects providing mental health services on a prepaid capitation basis to chronically mentally ill Medicaid beneficiaries. Requires any hospital receiving funds under titles XVIII or XIX to have a case plan established for, and a case manager assigned to such individuals prior to their discharge.

Treats certain chronically mentally ill individuals about to be discharged from an institution as presumptively disabled for purposes of title XVI. Extends the period during which certain institutionalized mentally ill may receive SSI benefits if such individuals are expected to return home upon discharge.

Provides Medicaid coverage for certain SSI recipients who are chronically mentally ill and would be institutionalized but for such coverage. Preserves the eligibility of such individuals for SSI benefits for the period during which they are in transitional living facilities.

Repeals limits on coverage of outpatient services relating to mental illness under part B (Supplementary Medical Insurance) of Medicare.