In this article author explores the law regulation of the institute of the special pre-trial investigation of criminal offenses considering the changes. The light is shed on the role of the public prosecutor in the context of motion trial during the special pre-trial investigation. The issue of introducing changes to the Chapter 241 of the Criminal Procedure Code of Ukraine is considered. The grounds for conducting the special pre-trial investigation or special court proceeding are analyzed. The legislative consolidation of the possibility of declaring international and/or interstate searching of a person is covered. The duty of the investigator (or the public prosecutor) regarding the proof of the fact that the suspect is hiding from the investigating authority aiming to evade the criminal liability (i. e. the suspected person has to know that there is a criminal case against him/her and he/she is notified of suspicion; however, he/she is hiding aiming to evade the criminal liability) is defined. Therefore, the investigating judge is obliged to take into consideration availability of sufficient evidence for suspicion of a person, towards which the motion for conducting of a special pre-trial investigation is filed. The trial of the motions for conducting of a special pre-trial investigation, special court proceeding of the offenses, mentioned in the Part 2 Art. 2971 of the Criminal Procedure Code of Ukraine is conducted by the court in according to the rules of jurisdiction, defined in the Art. 32 of the Criminal Procedure Code of Ukraine.