Rahman was Special Branch inspector, his wife Swapna a housewife.
Defence lawyer Mahabub Hasan Rana filed the plea at the court of Dhaka’s Chief Metropolitan Magistrate Court on Sunday.
Sep 5 has been fixed as the next hearing date for the petition.
Metropolitan Magistrate Bikas Kumar Saha has ordered police to produce Oishee before court on that day.
Bodies of Mahfuz and Swapna, bearing stab wounds, were recovered from their Chameligbagh residence on Aug 16.
Oishee, who had gone out of home a day before the date, surrendered to police on Aug 17 and was later send on police remand alongwith minor housemaid Khadiza Khatun Sumi.
Sumi is said to have assisted Oishee under pressure.
Police claim Oishee has already admitted killing her parents.
The remand has kicked off a barrage of criticism.
According to her school documents, Oishee is yet to be 18.
A Dhaka court ordered Oishee and Sumi to ‘Kishori Unnayan Kendra’, a juvenile correction home in Gazipur.
The case’s investigation officer on Aug 29 submitted Oishee's birth certificate which shows her to be over 18.
Metropolitan Magistrate Anwar Sadat ordered Oishee be transferred to Dhaka Central Jail.
As per the order, both Oishee and Sumi, a minor, were transferred to jail on Saturday.
Police had conducted several tests to ascertain Oishee’s age but the reports were not made public.
of domestic help Sumi is yet to be established.
None had so far reportedly turned out to see her.