Clean Start Act This bill amends the federal criminal code to establish a process to seal records related to a nonviolent criminal offense committed by an individual whose substance use disorder is a substantial contributing factor in the commission of the offense. A nonviolent criminal offense is a federal criminal offense that is not a violent offense, a sex offense, a serious drug offense, or an offense with a victim under the age of 18. To be eligible for sealing, an individual who is convicted of a nonviolent criminal offense must, among other things, complete a substance use disorder treatment program or recovery program and complete service in a substance use disorder peer mentorship program. This bill also amends the Omnibus Crime Control and Safe Streets Act of 1968 to allow the Department of Justice to give preference to a Community Oriented Policing Services program grant applicant from a state that has in effect: (1) a substantially similar law related to sealing adult records, or (2) a law that allows an individual who successfully seals a criminal record to be free from civil and criminal perjury laws.