Health officials there are reeling under intense pressure and are unable to handle the number of cases being brought to the facility as a result of the ongoing strike by the Ghana Medical Association.
Doctors in public health facilities across the country are on strike to back their demand for conditions of service.
Principal nursing officer at the hospital, Mary Doe, told Joy News' Francis Abban the emergency unit has only 20 beds but had 68 patients to care for at the time of the visit.
Some of the patients have been forced to lie on stretchers as the hospital tries desperately to care for the sick persons.
Mary Doe said they need beds and medical supplies to sustain healthcare delivery.
She confirmed about three patients lost their lives even before they could be attended to.
She suspects they must have been turned away from other health facilities before making their way to the 37 Military Hospital.
Meanwhile, the Health Minister Alex Segbefia has been touring some health facilities in the capital to see at first hand the impact of the doctors' strike.
He visited Korle Bu, Police and 37 Military hospitals on Wednesday from where Joy News' Matilda Wemegah reported that officials are breaking their backs to see the increasing number of patients who have trooped to the 37 and Police Hospitals.
The Minister advised patients to visit alternative health facilities like the Cocoa Clinic, Legon Clinic etc in order to reduce the pressure.