Police said they detained them to obtain information on the suspected student Shariful Islam and learn about his whereabouts.
Rajshahi Metropolitan Police Commissioner Md Shamsuddin on Friday said Shariful’s father retired school teacher Abdul Hakim, 63, and brother Ariful Islam, an 11th grader, were detained at Sreepur village of Bagmara Upazila.
He said Shariful has not been attending classes regularly for a year now.
The RMP chief also spoke about the three other murders and a bank robbery that took place in the city within a week.
A man and a woman, both university students, were found dead at a hotel in the city last Friday. Police said the female student was murdered.
Professor Siddiquee was hacked to death near his house the following day.
On Sunday, Rajshahi Awami League leader Ziaul Haque Tuku was found shot dead in his office on Sunday.
Police suspect the involvement of two Canada expatriates in the murder and asked the authorities to bar them from leaving the country.
On Thursday night, miscreants hacked a jeweller and robbed his shop before they fled, exploding bombs.