A PSNI spokesperson said: "Detectives are investigating the circumstances surrounding the sudden death of a woman in Portadown reported during the early hours of this morning (Tuesday, February 9th).
"A post mortem examination will take place in due course to determine the cause of death.
"A 50-year-old man has been arrested as part of the investigation and has been taken to Musgrave Custody Suite.
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"There are no further details at this time."
Upper Bann DUP MLA Jonathan Buckley said the death happened in the Carrickdale Gardens area of Portadown's Tandragee Road.
"It is very sad news. My heart goes out to this woman's family as they cope with their grief," he said.
MP Carla Lockhart said: "This is very sad news. A life lost, and those left behind will mourn that loss.
The PSNI will be holding the scene all of today and I know the community, which is in shock at this tragedy, will give them the space to conduct their investigations.”