A man has died in police custody, plunging nine floors to his death after officers were called about a break-in at a block of flats in inner Melbourne.

Police confirmed the death, which happened about 2pm today when the man fell from the ninth-storey balcony at the corner of Elgin and Nicholson Streets in Carlton - narrowly missing officers who had arrived at the scene to provide back-up for colleagues.

Homicide squad detectives are investigating and the ethical standards department will oversee the investigation, a police spokeswoman said.

Assistant Commissioner Stephen Fontana said police received a call about two men trying to break into a ninth-floor flat at the Carlton block.

At the same time, another call was made to police from somebody who claimed to be inside the flat that was being broken into, saying that two men were after him.