The bodies were found in their home in the city's Kotwali Thana area around 12pm on Sunday, police said.
The dead have been identified as Afsia Akter Ratna, her 22-month-old daughter ‘Nihan’ and one-year-old son ‘Nishad’.
Police have arrested Ratna’s husband Abdur Razzak in connection with the deaths.
“The preliminary investigation suggests that Razzak may have strangled his wife and kids to death over a family dispute before attempting to take his own life,” said Kazi Muttaki Ibnu Minan, deputy commissioner (crime) of Rangpur Metropolitan Police.
Police also suspect that Razzak is addicted to drugs, he added.
“Razzak has been taken to hospital for treatment. He will have to face interrogation later.”
According to Ratna’s elder sister ‘Shahnaz’, a dispute between the couple over money ended with Razzak killing his wife and two children.
“He recently got Tk 70,000 to buy an auto-rickshaw. He probably killed my sister over it.”
The authorities will take the next steps after an investigation into the incident, said Kotwali Police Station OC Abdur Rashid.