Investigators say evidence found at the south London property and a possible disturbance before the fatal fall led them to believe there were suspicious circumstances.
Renata Poncova and Tony Taylor, both aged 33, died after falling from the block where they lived together in Marchwood Close, Camberwell, late on 2 November.
Police had been called to the address shortly before midnight to reports that a man and woman had been injured in a fall.
Officers gave emergency first aid prior to the arrival of paramedics, but the pair were pronounced dead at the scene at 12.30am on 3 November.
A post-mortem examination found both had died as a result of multiple injuries “consistent with having fallen from height”.
While being treated as suspicious, police are not looking for anyone else in connection with the incident.
Detective Inspector Phil Coster said: “I am appealing for anyone who knew Renata Poncova and Tony Taylor, and had contact with them in the days before their deaths, to call police.
“I also need to speak with anyone who either witnessed the incident or saw anything suspicious either during on leading up to the deaths.
“Evidence at the flat and a possible disturbance at the flat prior to the fall leads us to believe there are suspicious circumstances.
“We need witnesses to come forward to help us build a picture of what happened before these deaths. If you know anything please call us.”
:: Anyone with information should call the incident room on 020 8358 0400 or 101 quoting reference CAD 9264/02NOV, or Crimestoppers anonymously on 0800 555 111.