Speedy Trials Assistance Act

Amends the Omnibus Crime Control and Safe Streets Act of 1968 to require a State applying for law enforcement assistance grants from the Law Enforcement Assistance Administration to include in its comprehensive State plans provisions designed to eliminate criminal case backlog, accelerate the processing and disposition of criminal cases, and improve the availability and quality of justice.

Requires that no less than one-third of such law enforcement assistance grants be distributed by the Administration in its discretion to further such goals. Grants funding priority to projects and programs dealing with such objectives.