Once you have reported the crime by filing an FIR, the officer in charge must send the report to a Magistrate, who will take note of the case without any unnecessary delay, and proceed with the investigation. This is a mandatory step that the police have to follow, as it allows the Magistrate to take control of the investigation, and if necessary give appropriate directions to the police.
The police will investigate the facts and circumstances of the case, and if necessary, take measures to find and arrest the person committing the crime. If the police officer feels that the case is not of serious nature, he may appoint a subordinate officer to do the investigation. Also, if they think that there are no sufficient grounds to investigate further, they may not do so.
When the Police are done with their investigation and have found enough evidence to proceed with a criminal case, they file a charge sheet. However, after investigation, if they have not found anything proving the commission of a crime, they will suggest closing the case by filing a closure report to the Magistrate.
It is the filing of the charge sheet where the trial of a criminal case begins. The police do not have a time limit to file the charge sheet or a closure report. Even the Magistrate cannot compel the police to file the charge sheet in a particular period of time. But if the person accused of a crime is in jail, then they have either 60 days (where the punishment for the crime is less than 10 years) or 90 days (where the punishment of the crime is more than 10 years) to file the charge sheet.