Medical workers collected specimens from her body and sent to the laboratory of the Institute of Epidemiology, Disease Control and Research or IEDCR in Dhaka for coronavirus test.
Yaseer Arafat, the assistant commissioner (land) in Jagannathpur Upazila, said he went to the village of the woman and ordered her relatives to remain in home quarantine for 14 days on Sunday.
They will be punished if they break the rules, he added.
The woman was admitted to the Sylhet Shaheed Shamsuddin Ahmed District Hospital
on Mar 20 after suffering from fever, cold, cough and breathing problems for 10 days.
The 61-year-old, who returned from London on Mar 4, breathed her last at the isolation unit of the hospital in the early hours of Sunday.
The woman was buried at a graveyard in Sylhet under the supervision of the IEDCR.
Representatives from the IEDCR were supposed to come to Sylhet on Sunday to collect samples from the patient.
However, she died before their arrival, Sylhet Civil Surgeon Premananda Mondol said.
The authorities then sent previously collected blood samples with saliva to the Dhaka lab.