Rape Kits and DNA Evidence Backlog Elimination Act of 2003

Expands the scope of DNA samples to be included in the Combined DNA Index System.

Authorizes the Attorney General to award grants to up to 15 State or local forensic laboratories to implement innovative plans to encourage law enforcement, judicial, and corrections personnel to increase the submission of rape evidence kits and other biological evidence from crime scenes.

Amends the Act to make local governments and Indian tribes eligible to apply for and receive DNA backlog elimination grants.

Requires the Attorney General to establish a program to award and disburse annual grants to SAFE (Sexual Assault Forensic Examination) programs, with priority to programs that are serving, or will serve, populations currently under-served by existing SAFE programs.

Authorizes the Attorney General to award grants to prosecutor's offices, associations, or organizations to train local prosecutors in the use of DNA evidence in a criminal investigation or a trial.

Eliminates the statute of limitations for child abduction and sex offenses. Provides that the limitation period in cases in which DNA testing implicates a person in the commission of a felony shall not preclude prosecution until an equal period has elapsed following such testing.

Amends the Violence Against Women Act of 2000 to cover dating violence.

Expresses the sense of Congress that the Paul Coverdell National Forensic Science Improvement Act should be funded in order to improve the quality, timeliness, and credibility of forensic science services for criminal justice purposes.