A division bench of the Supreme Court passed this reportable Judgment,

From Paras 10-12,

10.Ordinarily, Section 156(3) of the Cr.P.C. is invoked by the complainant when the police authorities decline to register a First Information Report. In such circumstances, a private complaint may be made in the court of the Judicial Magistrate and the complainant may pray that police investigation be ordered under Section 156(3) of the Cr.P.C. However, it is the discretion of the concerned Magistrate whether to order police investigation under Section156(3) of Cr.P.C. or take cognizance upon the complaint and issue process or dismiss the complaint under Section 203 of Cr.P.C. Over a period of time and in view of many decisions of this Court, if the officer in-charge of the concerned Police Station for some reasons declines to register the FIR, then the law has left it open for the complainant to file an appropriate application before the Magistrate and pray for police investigation. Once an order is passed for police investigation under Section 156(3) of the Cr.P.C., then it becomes a police case. At the end of the investigation the police may either file a charge-sheet or file an appropriate closure report.
11.However, what is important to observe is that whenever any application is filed by the complainant before the Court of Judicial Magistrate seeking police investigation under Section 156(3) of the Cr.P.C., it is the duty of the concerned Magistrate to apply his mind for the purpose of ascertaining whether the allegations levelled in the complaint constitute any cognizable offence or not. In other words, the Magistrate may not undertake the exercise to ascertain whether the complaint is false or otherwise, however, the Magistrate is obliged before he proceeds to pass an order for police investigation to closely consider whether the necessary ingredients to constitute the alleged offence are borne out on plain reading of the complaint.

From Paras 24 and 25,

24.Thus, there are prerequisites to be followed by the complainant before approaching the Magistrate under Section 156(3) of the Cr.P.C. which is a discretionary remedy as the provision proceeds with the word ‘may’. The Magistrate is required to exercise his mind while doing so. He should pass orders only if he is satisfied that the information reveals commission of cognizable offences and also about the necessity of police investigation for digging out of evidence neither in possession of the complainant nor can be procured without the assistance of the police. It is, thus, not necessary that in every case where a complaint has been filed under Section 200 of the Cr.P.C. the Magistrate should direct the Police to investigate the crime merely because an application has also been filed under Section 156(3) of the Cr.P.C. even though the evidence to be led by the complainant is in his possession or can be produced by summoning witnesses, with the assistance of the court or otherwise. The issue of jurisdiction also becomes important at that stage and cannot be ignored.
25.In fact, the Magistrate ought to direct investigation by the police only where the assistance of the Investigating Agency is necessary and the Court feels that the cause of justice is likely to suffer in the absence of investigation by the police. The Magistrate is not expected to mechanically direct investigation by the police without first examining whether in the facts and circumstances of the case, investigation by the State machinery is actually required or not. If the allegations made in the complaint are simple, where the Court can straightaway proceed to conduct the trial, the Magistrate is expected to record evidence and proceed further in the matter, instead of passing the buck to the Police under Section 156(3) of the Cr.P.C. Ofcourse, if the allegations made in the complaint require complex and complicated investigation which cannot be undertaken without active assistance and expertise of the State machinery, it would only be appropriate for the Magistrate to direct investigation by the police authorities. The Magistrate is, therefore, not supposed to act merely as a Post Office and needs to adopt a judicial approach while considering an application seeking investigation by the Police.

From Para 31,

31.A comparison of Section 175(3) of the BNSS with Section 156(3) of the Cr.P.C. indicates three prominent changes that have been introduced by the enactment of BNSS as follows:
a. First, the requirement of making an application to the Superintendent of Police upon refusal by the officer in charge of a police station to lodge
the FIR has been made mandatory, and the applicant making an application under Section 175(3) is required to furnish a copy of the application made to the Superintendent of Police under Section 173(4), supported by an affidavit, while making the application to the Magistrate under Section 175(3).
b. Secondly, the Magistrate has been empowered to conduct such enquiry as he deems necessary before making an order directing registration of FIR.
c. Thirdly, the Magistrate is required to consider the submissions of the officer in charge of the police station as regards the refusal to register an FIR before issuing any directions under Section 175(3).

From Paras 34-35,

34.In light of the judicial interpretation and evolution of Section 156(3) of the Cr.P.C. by various decisions of this Court as discussed above, it becomes clear that the changes introduced by Section 175(3) of the BNSS to the existing scheme of Section 156(3) merely codify the procedural practices and safeguards which have been introduced by judicial decisions aimed at curbing the misuse of invocation of powers of a Magistrate by unscrupulous litigants for achieving ulterior motives.
35.Further, by requiring the Magistrate to consider the submissions made by the concerned police officer before proceeding to issue directions under Section 175(3), BNSS has affixed greater accountability on the police officer responsible for registering FIRs under Section 173. Mandating the Magistrate to consider the submissions of the concerned police officer also ensures that the Magistrate applies his mind judicially while considering both the complaint and the submissions of the police officer thereby ensuring that the requirement of passing reasoned orders is complied with in a more effective and comprehensive manner.

Index of Judgments under Sec 156(3) Cr.P.C. are here.