Steven Parker, 23 and Kiran Creevy, 20, died shortly after police arrived at the Clyde Court block in Wortley.
The officers had been alerted shortly after 4am yesterday by someone at the address and were entering the flat as the apparent double suicide took place.
Mr Parker and Miss Creevy were pronounced dead at the scene.
The force has declined to comment further but the matter has now been referred to the police watchdog, the Independent Police Complaints Commission (IPCC).
An IPCC spokesman said last night: “We have received a referral by West Yorkshire Police and an assessment is ongoing to determine whether or not we will be involved in an investigation.
“No decision is expected until tomorrow at the earliest.”
Residents of Clyde Court reported hearing shouting and screaming in the build-up to the incident.
One neighbour, who wished to remain anonymous, said he had heard the couple arguing in their flat at about 3am.
He said: “They would argue regularly, I used to hear them. It’s so sad that it’s happened. They had lived there ever since I moved in a year ago.”
The door to the couple’s flat was guarded by a police officer yesterday and inside the flat appeared bare, devoid of any furniture, belongings or ornaments, the walls fully stripped.
A police forensic tent was set up at the base of the flats as an investigation started.
Resident Amanda Randle, 23, who lives on the second floor, said she heard the couple fall and looked out of her window to be confronted by the horrific scene.
She said: “I thought I heard a gunshot or someone throwing rubbish out.
“Then I looked out of the window and there were two bodies lying on top of each other.
“There was blood everywhere. He looked dead straight away.
“The woman was given treatment by paramedics, but she died too.”
Ms Randle’s partner Jason Small, 37, added: “I heard shouting and screaming, and the police actually arrived before the couple jumped. It was awful. ”
Another resident, Nicky Dibb, 20, said: “I heard the couple had sat on the window sill of their flat, and that they jumped out together holding hands.
“I heard the screams. It was just so shocking. You can still see the blood around the front door.”
But another resident, who wished to remain anonymous, said: “I heard a male voice saying ‘Don’t do it’ – then I saw the woman jump from the window.
“He didn’t jump until after the police arrived.”
One resident said suicide attempts had been a regular occurrence at the block, adding: “Something needs to be done – we’ve had three or four recently.”
Flowers had been laid at the flats entrance last night.
It is a matter of routine for the IPCC to investigate whenever police have been involved in a situation leading to the death of a member of the public.
A statement from West Yorkshire Police said officers had been concerned for the couple’s welfare.
It said: “At 4.08am police received a call from a flat in Clyde Court that made them concerned for the welfare of the two occupants.
“A short time later officers entered the property and a 20-year-old woman and a 23-year-old man fell from two windows to the ground below.
“Attempts were made to resuscitate them, but they were both pronounced dead at the scene.
“The circumstances surrounding their deaths are being investigated, however the deaths are not being treated as suspicious.
“Due to there having been police involvement immediately prior to the deaths, the force’s professional standards department has been informed, as has the Independent Police Complaints Commission.”