Another decomposing body was found on Sunday night in New Grant, Princes Town.
The dead person has been identified as 30-year-old Ketema Khanigh.
Police said his mother, Ann Ocho of Tobago, reported she last saw her son alive about three weeks ago at his home at Sixth Company Village.
She told them as she went into Khanigh's yard on Sunday evening, she saw the door to the house open, and there was a bad smell coming from inside.
Khanigh was lying on the floor in an advanced stage of decomposition.
Police said six spent shells were found next to the body.
An autopsy was expected to be done on Monday at the Forensic Science Centrein St James.
Homicide Bureau Region Three is investigating.