The Home Circuit court will decide on November 16 if Corporal Dwayne Smart will be granted bail.
Smart is charged with the murder of a pregnant woman in St Thomas two months ago.
His attorney Valerie Neita Robertson made the bail application when the case was called up today.
But Judge Martin Gayle said the decision on the matter would be made later this month.
Smart is facing the charges of murder, wounding with intent, assault, and illegal possession of a firearm.
He has been in custody since September 1 following the shooting death of Kay-Ann Lamont.
It is reported that Lamont and the policeman got into an altercation after he attempted to arrest her for using indecent language.
During the scuffle, Corporal Smart reportedly shot the pregnant woman twice in the head, killing her.
Corporal Smart then reportedly shot Lamontís sister in the shoulder.
Itís further reported that he attempted to shoot yet another sister but she escaped.