Supreme Court lawyer and also the resident of Shah Paran area in Sylhet, Syed Fazle Elahi filed the writ petition attaching a newspaper report.
The Secretary to the Home Ministry, Inspector General of Police, Sylhet Police Commissioner, Sylhet Deputy Commissioner, and Sylhet SP have been made respondents.
The HC bench of Justice Md Mozibur Rahman Miah and Justice Mohi Uddin Shamim is likely to hear the petition.
Rayhan Ahmed, 34, a resident of Akharia in Sylhet city, was beaten to death in police custody on Sunday, his family said.
His wife Tahmina Akter Tanni filed a case at Kotwali Police Station early Monday accusing a number of unidentified people.
Police rejected the allegation and said Rayhan was caught by locals of Kastghar area during robbery and was lynched.
The authorities on Monday suspended four policemen, including the in-charge of Bandarbazar Police outpost, over the incident.
Besides, the case has been transferred to the Police Bureau of Investigation, said Joytirmoy Sarkar.
Also read: Death ‘in Sylhet police custody’: 4 policemen suspended, 3 withdrawn