It is not possible to file the FIR with police and private complaint in court simultaneously. And, in fact, it is not needed also.
If the complaint discloses a cognizable offence (such as under Section 420 IPC, as you have stated), then you must first give the complaint to the police for registration of the FIR followed by investigation. If the police refuses to register FIR, then of course, you can file a private complaint with the Magistrate court, if you so wish, or approach the Magistrate under Section 156(3) of the Cr.P.C. for directing the police to investigate the case.
If the police registers the FIR but closes the case after investigation by filing a closure report (final report) under Section 173 of the Cr.P.C., then also you will get a chance to file your protest petition with the Magistrate against such closure, whereupon the Magistrate will either direct the police for further investigation or will take the cognizance of the case directly on the basis of the police report or will consider your complaint as if it were a private complaint or may close the case if you cannot satisfy the Magistrate about your case.
So, in either case, you’ll get an opportunity to proceed with your case even if police does not do justice with your complaint. Therefore, there is no need for filing a private complaint simultaneously along with the FIR. Moreover, as mentioned above, it is also not legally permissible to file both the things simultaneously, i.e., FIR with police and private complaint in court, together.
Dr. Ashok Dhamija is a New Delhi based Supreme Court Advocate and author of law books. Read more about him by clicking here. List of his Forum Replies. List of his other articles. List of his Quora Answers. List of his YouTube Videos.