On Monday, police officers took testimony from many eyewitnesses and relatives of the 33 year-old-woman, identified only as Ngo.
Her torso was found Sunday afternoon on the net covering the skylight at the Hoang Anh Thanh Binh apartment complex in District 7. Her head lay around two meters away.
Her younger sister told the police that she lived with Ngo in the same apartment on the 31st floor of the building.
The sister said Ngo had suffered from depression since 2013 and had consulted doctors at mental hospitals several times. The situation had improved recently, she added.
Around a month ago, Ngo opened a nail salon on Nguyen Van Quy Street in District 7 and soon after, started showing signs of being disheartened.
Weeks earlier, she had also lamented the pressures she was under and said she wanted to commit suicide. She also suffered severe psychomotor seizures, police said.
Autopsy results have confirmed Ngo died of multiple injuries, police said, adding that investigations are continuing.
In February 2018, a study released by the United Nations Children's Fund (UNICEF) said mental health and psychosocial problems were widespread and increasing in Vietnam, particularly among children and young people. It said that despite some progress, the mental health response system in the country remains largely inadequate to meet current requirements.
The lack of mental health services is particularly acute in remote provinces, the study found. The system has failed to prevent suicides and treat mental health disorders, which are often at the heart of suicidal ideation and attempts, the UNICEF report said.