The law-enforcers are looking into a possible conflict within the family of businessman Abdul Karim, among other angles, in the investigation into the murder of his first wife and their eldest son at their Kakrail home in Dhaka.
Police have detained a woman, Sharmin Aktar Mukta, and said she is the third wife of Karim, whose business concerns range from grocery to filmmaking.
They are also searching for his divorced wife.
Police could not arrest anyone until Thursday evening, 24 hours into the murders.
No case has been started yet. Police said the case would be initiated once a brother of Shamsunnahar, the murdered wife of Karim, arrived from Munshiganj.
Shamsunnahar was found slaughtered at their fourth-floor flat of the six-storey building owned by Karim on Wednesday evening.
Their youngest son Sajjadul Karim Shaon, 22, was found dead in a pool of blood on the staircase. Their two other sons live abroad.
Ramna Police Station Sub-Inspector Atwar Hossain, who made the first inquest reports, said there were marks of sharp weapon wounds on both the bodies, including their necks.
Asked about the motive behind the murders, Ramna Police Station OC Mayeenul Haque told bdnews24.com: "As Abdul Karim has married thrice, we are prioritising conflict in the family in the investigation."
He said they were also checking disputes in Karim's businesses and other issues in the investigation.
Dhaka Metropolitan Police Acting Deputy Commissioner Nabid Kamal told bdnews24.com: "Karim married Mukta four years ago after divorcing his second wife. We've detained Mukta for questioning."
"We are also looking for his divorced wife. She will also be questioned," he said.
A tenant of the building said he heard about 'some problems of Karim with the brothers of his third wife'.
Police officer Kamal could not confirm the issue.
According to Kamal, Karim has another son with his second wife, but no other with Mukta.
"We are investigating all the issues," he said.
On Thursday, police recovered the bodies of a man and his minor daughter at their flat in Badda.
DMP Joint Commissioner Krishnapada Roy told reporters that there was no link between the Badda and Kakrail murders.
"But it seems to me that disputes in the families, deprivation of someone from assets or tug-of-war over relationships may by behind both the murder incidents," he added.