Debdulal Rakhshit, brother of former sub-inspector Nandadulal of Teknaf police station, also an accused in the case, filed the writ petition on 8 September.
The writ sought HC directives restricting disclosure of details of the accused to the 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 to the home and information ministries were made respondents to the rule.
Major (retd) Sinha was killed in police firing at Baharchhara police check-post on 31 July.
Sharmin Shahriar Ferdous, elder sister of Sinha, filed the case with Teknaf senior judicial magistrate's court on 5 August.