State and Local Narcotics Control Assistance Act of 1985 - Authorizes the Attorney General to make grants to States to assist States and local governments to increase their drug enforcement activities. Requires such grants to be based on the relative needs of the States, taking into consideration the severity of drug trafficking and abuse and the availability of State and local resources to resolve such problems.

Establishes a procedure for grant applications. Requires such an application to include a State-wide strategy for the enforcement of State drug laws. Imposes limitations on the use of such grants, including a maximum ten percent allocation for administrative purposes.

Requires each State which receives a grant to submit a yearly report to the Attorney General, who shall in turn report to the Congress with respect to such grants.

Allows the Secretary of Health and Human Services to make grants to States for developing more effective drug abuse prevention, treatment, and rehabilitation programs. Establishes a procedure for grant applications.

Authorizes appropriations for both grant programs for FY 1986 through 1990.