Rural Safety Act of 2003 - Amends the Omnibus Crime Control and Safe Streets Act of 1968 to: (1) authorize the Attorney General to make grants to rural local and tribal governments for the retention for one additional year of police officers funded through the cops on the beat (or COPS) Program; and (2) authorize the use of COPS grants on a matching funds basis to assist the police departments of such units in improving police communications, and in developing and improving access to crime-solving technologies.

Directs the Office of Justice Programs of the Department of Justice to make grants to such units to: (1) establish or improve 911 service in those communities; and (2) establish restorative justice programs for juveniles, such as victim/offender mediation and family and community conferences.

Amends the Public Health Service Act to require the Secretary of Health and Human Services, acting through the Director of the Center for Substance Abuse Treatment, to make grants to establish in rural areas substance abuse (particularly methamphetamine) prevention and treatment pilot programs and methamphetamine prevention education programs.

Directs the Attorney General to provide for the cleanup of methamphetamine laboratories and related hazardous waste, and for the improvement of contract-related response time for cleanup of methamphetamine laboratories and related hazardous waste by providing additional contract personnel, equipment, and facilities, in rural areas.

Establishes a Rural Policing Institute as part of the Small Town and Rural Training Program.