Fresh Start Act of 2013 - Amends the federal criminal code to allow an individual convicted of a nonviolent criminal offense to file a petition for expungement of the record of such conviction. Allows expungement if such individual: (1) has never been convicted of any criminal offense other than the nonviolent offenses committed in a single criminal episode that includes the offense for which expungement is sought; (2) has fulfilled all requirements of the sentence of the court, including payment of all fines, restitution, or assessments and completion of terms of imprisonment and probation; and (3) has remained free (if required by the court's sentence) from dependency on or abuse of alcohol or a controlled substance for at least one year.

Requires the Attorney General to maintain an unaltered nonpublic copy of expunged criminal records, to be disclosed for limited purposes to federal, state, or local law enforcement agencies.

Amends the Omnibus Crime Control and Safe Streets Act of 1968 to increase by 5% grant funding under the Edward Byrne Memorial Justice Assistance Grant Program to states that implement expungement procedures substantially similar to the procedures enacted by this Act. Decreases such grant funding by 5% for states that fail to adopt expungement procedures.