WPC Nyasha Joseph, a mother of a 4-year-old child, did not show up for work on Thursday and relatives and co-workers were unable to contact her.
Her body was discovered in the Beetham on Friday morning. She had been shot.
Police have held a man who had been in a relationship with Joseph. He was taken to the Besson Street Police Station, where he is being questioned. Joseph’s body was removed to the Forensic Sciences Center, Federation Park for an autopsy.