Shaikat was produced before a Dhaka court by police on Sunday
In their remand petition, police have said their initial suspicion is that the suspect Shaikat, Rumpa's former lover, and his cohorts murdered Rumpa by pushing her off a building in Shiddheswari.
The investigation officer of the case Detective Branch police Inspector Shah Mohammad Akhtaruzzaman submitted a remand plea to the Dhaka Metropolitan Magistrate Mamunur Rashid's court on Sunday.
Police requested a seven day remand for Shaikat so that during interrogation police can uncover the actual reason of her murder and find out who else were involved with it.
According to the petition, Rubaiyat Sharmin Rumpa met her former boyfriend Shaikat near the Shiddheswari campus of Stamford University on the night of her death.
The report says they got into a major argument when Shaikat told Rumpa that he wanted to break off their relationship.
Later, Shaikat and his men took Rumpa to a building near Sidhheswari's Circular Road around 10:45pm on Wednesday, and pushed her off the building, the plea said.
Earlier in the day, Shaikat was produced before court by police along with the remand plea. The court took the request into cognizance and placed Shaikat on a four day remand.
The court also rejected his bail petition, Shaikat's lawyer Abdul Hamid Bhuiyan told Dhaka Tribune.
Shaikat's mother, who was present at the court, told reporters that Shaikat turned himself in to the police when he was asked to make an appearance to the police station.
The law enforcement agency detained Saikat, said to be Rumpa's former lover, for interrogation on Saturday night.
On December 4, police recovered the body of Rumpa, 21, a second year student at Stamford University's English department, from 68 Siddheswari Circular Road, behind Ayesha Complex around 11pm.
Police sent her body to Dhaka Medical College Hospital (DMCH) morgue as an unidentified one. Later, her family members identified the body on Thursday evening.
A murder case was filed in this regard with Ramna police station in this connection on December 5.
Claiming that Rumpa, daughter of police Inspector Rokan Uddin, was murdered, her family members and fellows demanded arrest of the perpetrators.