Refugee Assistance Extension Act of 1985

Refugee Assistance Extension Act of 1985 - Amends the Immigration and Nationality Act to authorize FY 1986 and 1987 appropriations for refugee assistance.

Requires an agency receiving initial resettlement grants to: (1) provide quarterly performance and finance reports; (2) notify local welfare offices when a refugee is offered employment; (3) notify, upon request, local welfare offices of any cash assistance provided directly by such agency to a refugee; (4) assure that refugees with medical conditions affecting the public health report to the appropriate health agency in their resettlement area; and (5) fulfill its responsibility to provide the basic needs of each refugee.

Requires the Federal agency administering the program of initial resettlement to establish criteria for the performance of agencies receiving such grants.

Provides cash and medical assistance for refugees who would otherwise be eligible for aid to families with dependent children or medical assistance under title XIX (Medicaid) of the Social Security Act. Terminates refugee cash assistance for three months for refusal to accept employment (six months for subsequent refusals).

Prohibits: (1) such cash or medical assistance grants from being given as block or consolidated grants; or (2) the Director from delegating grant review or approval authority to the States or their political subdivisions. Permits per capita grants to be made available to States if requested and used for demonstration projects.

Directs the Attorney General to pay compensation to States and counties for costs incurred in incarcerating certain Cuban nationals who were allowed U.S. entry in 1980 and who were subsequently convicted of violating State or county law.