Police on Tuesday said a woman arrested in connection with a murder case on Cheung Sha Wan Road the day before was under tremendous stress.

"She revealed that she came under a lot of emotional stress recently and was struggling to cope with it," said acting superintendent Cheng Ki-fung from the Sham Shui Po crime division.

Officers also said the 52-year-old suspect, who has a history of mental illness, told them she'd harboured suicidal thoughts.

Her 85-year-old mother and 47-year-old brother were found dead in a flat at Hang Moon Building on Cheung Sha Wan Road on Monday.

The mother was found to have four wounds in her neck and the brother, who had Down syndrome, had been suffocated.

The suspect was found by police sitting at the edge of the building's roof and pulled back to safety by emergency personnel.