Another accused is Tanvir Hasan Shaikat, general secretary of Dhaka University's Bangladesh Chhatra League (BCL) unit.
Dhaka Metropolitan Magistrate Md Rashidul Alam passed the remand order on Thursday after Sub-inspector Md Yusuf, the investigation officer of the case, produced them before his court with a remand petition.
Law enforcers claimed that they arrested Tuku, Palak and Shaikat in Nikunja residential area of the capital on Wednesday.
The media wing of the Dhaka Metropolitan Police said the trio was hiding there. Later, they were shown arrested in the case filed with the Paltan Police Station.
Earlier on August 6, the day after the fall of the Sheikh Hasina-led government, Palak was detained at Hazrat Shahjalal International Airport while he was trying to flee the country.
Officials at the airport said Palak had been handed over to "a force".
Fatema Khatun, wife of Kamal Mia, filed the case on July 20 against some unidentified assailants.
According to the case statement, Kamal was waiting for passengers near the VIP Road intersection in Paltan around 7:30pm on July 19.
A little later, Fatema came to know from a neighbour that her husband was lying on the road in a pool of blood.
Fatema and her daughter went there and took Kamal to Dhaka Medical College Hospital, but doctors declared him dead, it reads.
In the remand prayer, IO Yusuf said involvement of the accused with the incident was primarily proved.
Moreover, on their direction, the other accused committed such offences. So, they need to be remanded to find out the vital clues about the whereabouts of others responsible for committing such offence, he said in his forwarding report.
Defence lawyers sought bail along with the cancellation of the remand petition.
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