One resident of the building told the Herald the death had occurred on the seventh floor of the building. Another neighbour across the road had no knowledge of the incident when approached by the Herald.
A scene guard had been in place as police investigated.
But a police spokesperson has now confirmed they are not treating the death as suspicious.
“Police are not seeking anyone in relation to this incident and the matter has been referred to the coroner,” they said.
The housing complex is the same one where a dead pensioner lay undiscovered for almost a year, and was the scene of a murder in 2010.