Oishee decided to kill her parents after they had taken away her mobile phone on July 31.
They also kept her confined to house as they came to know about her bad company and drug use.
The 17-year-old girl said all this to detectives.
Around 4:00pm on Friday, the decomposing bodies of Special Branch police inspector Mahfuzur Rahman and his wife Swapna Rahman were recovered from their Chamelibagh residence in the capital.
Twenty-two hours later, their teenage daughter showed up at Paltan Police Station. Her friend Mizanur Rahman Rony and house help Khadiza Khatun Sumi were arrested the same day.
Yesterday, a Dhaka court placed the trio on a five-day remand so that police can try to know if anyone instigated the murder.
A sad and devastated Oishee told reporters at the court she disclosed to police the motive of the murder and the names of those involved in it. She would not elaborate further.
“Her parents had imposed restrictions on her movements for over a month before the incident. On July 31, they took away her mobile phone,” Dhaka Metropolitan Police Joint Commissioner Monirul Islam told reporters at the DMP media centre yesterday.
Earlier, a press briefing was held at the media centre regarding the murder.
The couple did not to keep knife and sharp objects at their house because they feared Oishee might do something violent, Sumi told police during interrogation.
“Sumi claimed that the knife Oishee used for the murder was not from the house,” Monirul said. Earlier, a bloodstained knife and a kitchen knife were recovered by police from the crime scene.
On Wednesday evening, Oishee served her mother Swapna a cup of coffee mixed with two sedatives tablets. Swapna soon fell asleep in her bedroom.
Later, around 10:00pm, Oishee called her father Mahfuz from her mother's mobile phone and requested him to come home early.
As he came home, she served him with the sedative-mixed coffee. Mahfuzur fell asleep in his daughter's room.
Monirul said Oishee carried out the murders around 2:00am, starting with her father. She then attacked her mother but Swapna woke up shouting, also waking up Oihee, who was sleeping beside her.
While struggling with her daughter, Swapna pushed away her son to save him.
The official added that Oihee, 8, who was taken to DB headquarters for quizzing, told them he remembers Oishee stabbing her mother. But the traumatised child is still unaware of his parents' death.
Locking her brother in the toilet attached to Swapna's bedroom, Oishee later put the bodies in her bedroom's toilet with help of Sumi, who told detectives that she was threatened by Oishee to help her.
Sumi, aged 10-12, also told detectives that she had seen Oishee mix something with the coffee in the evening.
After the murder, changing the SIM card of her mother's phone, Oishee had contacted several people, including Rony and two more male friends.
Rony helped her stay at his aunt's house in the city on Friday night.
Police came to know that the two other male friends assured Oishee that they would help her escape to India.
But later, another friend advised her to surrender to police because the other two might put her life in danger, a police source told The Daily Star.
Oishee had left home in a CNG-run auto-rickshaw on Thursday morning with Oihee, Sumi and two bags of valuables, including gold ornaments.
Oishee's maternal uncle Rabiul said she roamed around throughout Thursday, finally leaving Sumi at a slum in Aftabnagar, while she and brother spent Thursday night at her friend's house in Kakrail.
Later, sending her brother home in a rickshaw on Friday morning, she moved around before going to the house of Rony's aunt. Exhausted, she appeared in Paltan Police Station on Saturday afternoon.
Police interrogated at least 12 people in connection with the murder. Detectives detained Parvez, another of Oishee's friend yesterday afternoon for quizzing.
Monirul told reporters that Oishee is not consistent in her statements and often deviates from the topic.
At the beginning of the interrogation, the girl was even saying she just mixed sedatives with the coffee and two of her friends killed her parents. Later, she changed the version.