Senior sergeant Tim Crawford said the car, driven by Mr Gleeson, veered off the left-hand side of the road and struck a power pole, knocking it down.
The accident happened about 1am and power was cut in the Hokitika Valley for a time.
Mr Crawford said a scene examination was under way and would give police a better idea of what happened.
"Speed is possibly a factor, and it is unknown at this point whether alcohol was a contributing factor," Mr Crawford said. Road conditions at the time were wet, but not icy.
Friends of the pair later paid a tearful visit to the crash scene as news of the fatality emerged.