An 83-year-old man was found hanging inside the flat, as his wife, 85, lay passed out in the same room.
Both were later certified dead at Ruttonjee hospital.
Police say their 54-year-old son made the discovery at the apartment on Fort Road at around 7pm on Saturday night.
The deceased man was said to have expressed unhappiness about his domestic situation before his death. It’s understood his wife had Parkinson’s disease.
Authorities say they don’t yet know the cause of death for the woman, and post-mortem examinations will be carried out.