Spokesman Pervez Mir told a news conference that further investigations were being carried out by a toxicologist and a histologist (scientist who examines body tissue).
Mark Shields, deputy commissioner of the Jamaican police constabulary (crime division), said that the body could not be released until the pathologist had completed his examination.
"I know that the scientists are treating it with the utmost urgency in order that we can hopefully repatriate the body to his family as soon as possible," said Shields.
Asked when the scientists' conclusions would be available, Shields replied: "I just know they are working as quickly as possible to provide the information that we need. I hope it's today but it could be tomorrow."
He added that it was quite normal for there to be delays over a post mortem findings and refused to speculate on the causes of the death.
The police said he died in hospital at 12:14 p.m. local time (2240 IST) on Sunday.
Woolmer, 58, was found unconscious in his Kingston hotel room on Sunday after his team had been eliminated from the World Cup by debutants Ireland less than 24 hours earlier.