What rights do I have if the police refuse to register my complaint?

If your complaint relates to a cognizable offence, police are generally obligated to register an FIR — refusal to do so is itself a violation of their duty. You can escalate by approaching a senior police officer (such as the Superintendent of Police) directly, who has the authority to direct that the FIR be registered if satisfied a cognizable offence is disclosed.

If this doesn't work, you can approach the jurisdictional magistrate with an application under the relevant provision, requesting a direction to the police to register and investigate the FIR — magistrates have the power to give this direction where satisfied the complaint discloses a cognizable offence.

You can also register what's called a "Zero FIR" at any police station, regardless of where the offence actually occurred, if you're facing jurisdictional excuses for the refusal — this is specifically meant to prevent victims being turned away on those grounds. Keeping a written record of your attempts to file the complaint (dates, what you were told) will help if you need to escalate through these channels, ideally with a lawyer's guidance.