According to initial reports, officers of the Port of Spain CID received a call at about 12:30am indicating that a man had been seen lying on the ground in Victoria Square, bleeding from an injury.
A team of officers responded and the wounded man was rushed to the Port of Spain General Hospital.
However, while undergoing treatment, the man succumbed to his injuries.
His injuries appeared to be gunshot wounds.
An autopsy has since been ordered to confirm the cause of death.
Police said the man identified himself as David Cooper. A source said Cooper was employed with the Central Statistical Office (CSO).
Crime scene investigators returned to Victoria Square later in the day and searched the square for spent shells.
More on this as it becomes available.
In a separate incident police are investigating an incident in which a man was stabbed to death in St Augustine.