Zafar Sadique, 23, son of CID's Additional Deputy Inspector General (ADIG) Mozammel Hossain, has already walked free on bail.
Buying house official Mrityunjoy Acharya Mithu, 48, was run over by a car on Thursday at Banani's Chairmanbarhi.
ADIG's son Sadique, who was driving the white private vehicle sporting a 'police' tag, had no driving licence either, police said.
Mithu's brother Ujjal Acharya has filed a case in connection with the incident. He claims there are attempts to hush up the incident.
North South University student Sadique's involvement in the hit-and-run case came to light after a picture of a white car, sporting police tag, went viral on the social media.
He was detained and produced in court.
Speaking to bdnews24.com, plaintiff Acharya claimed they had refused cash offers to sweep the incident under the rug.
"Police officer Mozammel Hossain, too, tried to cover up by saying 'what is done, cannot be undone’," he alleged.
He said the ADIG had come to their Kazirparha residence on Sunday during his brother's 'Sharddha' or a ritualistic death ceremony.
"He (ADIG Hossain) came to our house suddenly and left after about 10 minutes.
"My two nieces shouted at him, 'your son has killed our father', before breaking down in tears," Acharya said.
He further claimed they had been given a proposal to settle the matter for Tk 300,000 when his brother's body was kept at the Dhaka Medical College and Hospital.
"We rejected the proposal. Our family demands Zafar Sadique's punishment for this incident," he added.