Wonderful judgment clearly states how law takes care of scenarios where the Police do not investigate a complaint/FIR.

Rule-1

If, notwithstanding the First Information Report, the officer-in-charge of a police station decides not to investigate the case on the view that there is no sufficient ground for entering on an investigation, he is required under sub-section (2) of Section 157 to notify to the informant the fact that he is not going to investigate the case because it to be investigated.

Rule-2

Then again, the officer in charge of a police station is obligated under sub-section(2)(ii) of Section 173 to communicate the action taken by him to the informant and the report forwarded by him to the magistrate under subsection (2)(i) has therefore to be supplied by him to the informant.

Rule-3

Now, when the report forwarded by the officer-in charge of a police station to the Magistrate under sub-section (2)(i) of Section 173 comes up for consideration by the Magistrate, one of two different situations may arise. The report may conclude that an offence appears to have been committed by a particular person or persons and in such a case, the Magistrate may do one of three things:
(1) he may accept the report and take cognizance of the offence and issue process or
(2) he may disagree with the report and drop the proceeding or
(3) he may direct further investigation under sub-section (3) of Section 156 and require the police to make a further report.

Rule-4

The report may on the other hand state that, in the opinion of the police, no offence apppears to have been committed and where such a report has been made, the Magistrate again has an option to adopt one of three courses:
(1) he may accept the report and drop the proceeding or
(2) he may disagree with the report and taking the view that there is sufficient ground for proceeding further, take cognizance of the offence and issue process or
(3) he may direct further investigation to be made by the police under sub-section (3) of Section 156.

Opportunity of filing Protest Petition

We are accordingly of the view that in a case where the magistrate to whom a report is forwarded under sub-section (2)(i) of Section 173 decides not to take cognizance of the offence and to drop the proceeding or takes the view that there is no sufficient ground for proceeding against some of the persons mentioned in the First Information Report, the magistrate must give notice to the informant and provide him an opportunity to be heard at the time of consideration of the report.

And finally,

It was urged before us on behalf of the respondents that if in such a case notice is required to be given to the informant, it might result in unnecessary delay on account of the difficulty of effecting service of the notice on the informant. But we do not think this can be regarded as a valid objection against the view we are taking, because in any case the action taken by the police on the First Information Report has to be  communicated to the informant and a copy of the report has to be supplied to him under sub-section (2) (i) of Section 173 if that be so, we do not see any reason why it should be difficult to serve notice of the consideration of the report on the informant. Moreover, in any event, the difficulty of service of notice on the informant cannot possibly provide any justification for depriving the informant of the opportunity of being heard at the time when the report is considered by the Magistrate.

Citation : [1985 AIR SC 1285], [1985 SCALE 1 1194], [1985 SCC CRI 267], [1985 SCC 2 537], [1985 CRLJ SC 1179], [1985 CRIMES SC 1 994], [1985 SCR 3 942], [1986 ACR SC 10 26], [1986 AWC SC 26], [1985 BOMLR 87 421], [1985 PLJR 53], [1985 SHIMLC 260], [1985 UJ 17 820], [1985 CRI LJ 1521], [1985 UJ SC 820]

Other Sources :

https://indiankanoon.org/doc/118375/

https://www.casemine.com/judgement/in/5609ac18e4b014971140e050