Blindly obeying any policeman takes us one step closer towards a "Police State", and one step farther from a healthy democracy. Therefore, our FUNDAMENTAL DUTY ("to develop a scientific temper, humanism, and spirit of enquiry and reform") requires us to overcome our blind fear of the uniform and fear of authority, and understand the limits of a policeman's powers. We need to understand what the law requires us to do, or not to do.
It is true that the law requires us to cooperate with a policeman in the performance of his duty. However, the law also requires us to UNDERSTAND THE LAW itself, and what it empowers the policeman to do.
If the policeman is acting in excess of his statutory powers, the law requires us to resist. A citizen's blind compliance with authority enables to State to encroach on the rights and privileges of all citizens.
Regardless of his rank, if a cop phones us and asks us to meet him at the police station, there is ABSOLUTELY NO NEED TO COMPLY. Tell the cop to give you a "summons" in writing i.e. write it and have it delivered to you. By doing so, you will be forcing him to create written records of his interaction with you, and prevent him from fishing for information without sufficient basis.
Please note: unless the police have registered a FIRST INFORMATION REPORT (FIR), they have ZERO POWERS TO INVESTIGATE anything in any connection. In other words, a policeman can neither visit a person nor phone a person "in connection with a criminal offence", until and unless that a criminal offence has first been registered as an FIR. All his powers emerge from a First Information Report.
Even if they have registered a non-cognizable offence (NC) against you or anybody else, the cops have no powers to investigate you, phone you or arrive at your doorstep.
If cops arrive at your doorstep without a summons and copy of FIR, there is absolutely no need for you to entertain them. You don't have to let them into your living room, and you don't have to go with them to the police station, and you don't have to say anything to them, orally or in writing.
If you blindly comply, you are laying yourself open to intimidation and exploitation by the police.
Merely receiving a written or oral complaint (against you or anybody else) DOES NOT EMPOWER THE COPS TO INVESTIGATE, until and unless they register an FIR. In other words, they cannot interrogate you, call you to the police station or anywhere else, or even detain you.
Please remember, the police can and will use any information that you give them (including a narration of events, or names of persons) AGAINST YOU IN A COURT OF LAW. No law compels you to give them ANY information, because no law compels you to incriminate yourself or "bear witness against yourself". Your story -- whether true or false -- enables the cops to formulate theories about how the criminal offence was committed, and to implicate you in a court of law. So you can choose to remain silent; that is not an offence.
And in the event that you have given the police a written and signed statement BEARING TESTIMONY AGAINST YOURSELF, and you come to realize it later, please remember that you can TOTALLY DISOWN IT later on in a court of law. Because a statement given to the police -- under duress or otherwise -- is inadmissible in a court of law UNLESS YOU OWN IT UP AND ACCEPT IT IN THE COURT OF YOUR OWN FREE WILL AND VOLITION.
[Advocates and other knowledgeable friends are encouraged to correct me by citing the correct CrPC sections if I am wrong in any respect.]