The tragedy occurred at a building on Via Novaro, in the Affori area of Milan, shortly after midnight on Monday, Il Fatto Quotidiano reported.
The woman died instantly while the man died later at San Girardo di Monza hospital.
Neighbours reportedly heard screams with one, a British model, saying the man appeared to have “dragged” the woman down. Another neighbour said: “I heard cries for help, the voice of a girl screaming.”
The man, who is said to have been an Italian of Brazilian origin, reportedly also tried to throw himself from the building a few months ago.
“He stood there for about an hour,” Franco, another neighbour was quoted by Il Fatto as saying. “Then a policeman distracted him while another one grabbed him. He was adopted and seemed like such a good boy. His family was wealthy and did not have money problems. I always used to see him in the area.”
Police are investigating.