They said that at about 11.15am on Tuesday, a 45-year-old woman told them that her younger sister had collapsed in a unit in Ting Tak House in On Ting Estate.
Police said they found the 42-year-old woman unconscious on a bed with neck injuries. She was certified dead at the scene.
Officers later found the woman’s 56-year-old boyfriend unconscious inside the unit, and he was sent to Tuen Mun Hospital.
Police say they arrested the 56-year-old man for murder on Friday afternoon and allege that he attacked the woman, covering her nose and mouth with plastic tape. He remains in custody.
They said a post-mortem has failed to establish the cause of death and further tests will be carried out.