The Ambulance Service said it was called to the Levaghery Gardens area of Portadown at 4.53pm on Wednesday after reports of an unconscious man.
One elderly female patient was taken to Craigavon Area Hospital. Both of them were in their eighties.
Police told the News Letter tonight that detectives are investigating the circumstances surrounding the death.
A woman aged in her eighties, who was also present in the house, was taken to hospital, where she remains at this time, a PSNI spokeswoman said.
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Detective Chief Inspector Eamonn Corrigan said: “Detectives are working to establish the full circumstances surrounding this death.
“At this stage we do not believe anyone else was involved in this incident. Our enquiries are continuing.”
As part of the response, the Ambulance Service tasked a Hazardous Area Response Team (HART) to the incident, which would usually deal with dangerous chemical or gas leaks.