Sharmin Shahrier Ferdous, elder sister of Sinha, filed the case at Teknaf Senior Judicial Magistrate Court on Wednesday, said senior lawyer Mohammad Mostafa.
Suspended Inspector Liakat Ali of Baharchhara police outpost and Officer-in-Charge of Teknaf Police Station Pradeep Kumar Das were among the accused.
Teknaf Senior Judicial Magistrate Tamanna Farah asked the authorities concerned to submit the probe report within seven working days.
Rapid Action Battalion (Rab) will investigate the case.
Sinha was killed in police firing at Baharchhara police check-post on July 31.
Two people were arrested and two separate cases were filed in this regard, Superintendent of Police ABM Masud Hossain said Saturday.
The Home Ministry formed a four-member committee, headed by Mizanur Rahman, additional divisional commissioner (development), on August 2.
The authorities on Sunday suspended 21 police officers, including the in-charge of Baharchhara police outpost, in connection with the killing.
Prime Minister Sheikh Hasina on Tuesday assured the mother of Major Sinha of proper investigation into the murder of her son and the trial of his killers.
PM’s Press Secretary Ihsanul Karim said the Prime Minister called up Sinha’s mother and consoled her.