Criminal Trial Procedure in Non-cognizable offences

Hello, What is the Criminal Trial Procedure in Non-cognizable offences having punishment upto 3 years. offences having more than 2 year of punishment are summon cases and offences having punishment more than 2 years are warrant cases. In a case where the punishment is more than 2 years (being warrant case) but the offence is non-cognizable. In such case, should the criminal complaint be directly file before magistrate u/s 190 crpc or first i have to file complaint u/s 155 crpc before SHO and then seek direction from magistrate u/s 155(2)crpc for conducting investigation? Thanks