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Police and medics were called to High Street, Sheerness, following the death of a woman in her 50s.
Officers were sent to the flat, believed to be near the Oxfam charity shop, at around 1.30pm yesterday.
A police spokesman said there were no suspicious circumstances and a report has been prepared for the coroner.
A witness, who asked not to be named, said there were several police and ambulance vehicles at the scene.