The writ was filed with the bench of Justice Md Khasruzzaman and Justice Md Mahmud Hassan Talukder while the court fixed September 13 for hearing on the petition.
Advocate Ahsan Ullah and Sajal Mahmud stood for the writ petitioner while Deputy Attorney General Bipul Bagmar represented the state.
Debdulal Rakhshit, brother of former Sub-Inspector Nandadulal of Teknaf Police Station, also an accused of the case, filed the writ petition on September 8.
The writ sought HC directives restricting disclosure of details of the accused to media until the investigation is concluded.
The petition also sought HC rule seeking explanation as to why publishing investigation details of the case should not be declared illegal.
Secretaries of the Home Ministry and Information Ministry were made respondents to the writ petition.
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Major (retd) Sinha was killed in police firing at Baharchhara police check-post on July 31.
Sharmin Shahriar Ferdous, elder sister of Sinha, filed the case with Teknaf Senior Judicial Magistrate’s Court on August 5.