Wellington Free Ambulance, which was alerted to the incident by a member of the public, said lifeguards used a defibrillator on Ms Groom before ambulance staff arrived.
Paramedics gave her further medical treatment, including more defibrillator treatment, but it was to no avail.
Police and the fire service also attended the incident.
Wellington police spokesman Nick Bohm said "a considerable amount of time" was spent by emergency services and the registered nurse trying to revive Ms Groom.
"At this stage there are no suspicious circumstances around the death. It looks like she has come to grief while in the water, rather than a drowning."
The pool was reopened late this morning.
Ms Groom's family have been advised of her death, and her case had been referred to the Coroner, police said.