As I have pointed out in my answer to a similar question – Time limit to complete investigation in FIR, generally speaking, the law does not prescribe any maximum time period for completion of investigation and filing of charge sheet. Please read that answer for more details and to learn about the exceptions.
You have not mentioned about the nature of your case. But, as I mentioned above, generally speaking there is no time limit to complete investigation. It depends on the nature of the case. Some offences need longer periods of time to complete the investigation, such as economic offences and documentary type cases.
FIR will remain valid and it does not lapse with time. On completion of investigation, police has to file either a charge sheet or a closure report in the court under Section 173 of the Criminal Procedure Code. Till that time, the investigation is considered to be ongoing and validly being done.
As regards arrest, it is not mandatory for the police to arrest the accused person in each and every case. It again depends on the nature of the case and also on the facts and circumstances of each individual case. In fact, nowadays, after the amendments to the Cr.P.C. made in the year 2009/2010, it has been made more difficult for police to arrest a person who is involved in an offence where the maximum punishment prescribed under law is up to 7 years imprisonment; the arrest powers of police in such cases are now curtailed to some extent.
Dr. Ashok Dhamija is a New Delhi based Supreme Court Advocate and author of law books. Read more about him by clicking here. List of his Forum Replies. List of his other articles. List of his Quora Answers. List of his YouTube Videos.