Arrangements for the implementation of restorative justice for adult offenders in Indonesia have different standards and requirements between law enforcement agencies, for example, the Police interpret the implementation of restorative justice in the form of peace between the parties and then, on the basis of this peace, a Letter of Order to Stop Investigation (SP3) is issued. Therefore, it is necessary to study further regarding the authority of the Police in handling and terminating cases based on restorative justice. This research is normative research carried out by analyzing norms in statutory regulations and concepts related to restorative justice. The conclusion is that the implementation of restorative justice in the Police is part of the Police's discretionary authority if restorative justice is interpreted as a technique for handling cases with an approach that prioritizes recovery by involving the perpetrator, victim, victim's family, perpetrator's family and impartial third parties. Meanwhile, the issuance of SP3 based on restorative justice is an inappropriate interpretation of the Police's discretionary authority because the SP3 has been integrated in a limitative manner in Article 109(2) of the Criminal Procedure Code.