They said they received a report at about 6am on Friday that a man was dragging an object outside 70 Tin Ha Road.
They said they found a 25-year-old man with the 30-year-old woman, who was his girlfriend.
Police said the woman had head injuries and multiple bruises, and was certified dead at the scene.
Police said they believe she was attacked in a unit on Tin Ha Road. The man is being detained for questioning.