Zodoq Obatolah, 52, sustained fatal injuries after falling from a fifth floor balcony in Rye Hill Park in the early hours of April 12.
Officers were called to the property just before midnight to reports of a man shouting from a balcony. However, they received no response from inside the flat and left.
At around 1.25am the following day, officers received a further report of a man making threats to jump from a balcony.
The Independent Office for Police Conduct (IOPC) said police forced entry to the property at around 2am and tried to persuade the man to come inside and requested a police negotiator attend the scene.
Over the course of the next hour, some officers left the flat and two officers remained inside – with evidence indicating an officer discharged their Taser, shortly before the man fell from the balcony railing at around 3.20am.
The man was transported to hospital with critical injuries but died later that day, the IOPC said.
The police negotiator arrived at the scene just before the man fell and had not entered the flat, the watchdog added.
They have also been served with gross misconduct notices for potentially breaching police standards of professional behaviour, but the IOPC stressed this does not necessarily mean that criminal charges or proceedings will follow.
The IOPC have issued an appeal to the public to identify any relatives of Zodoq.
IOPC regional director Mel Palmer said: “While it is positive that Mr Obatolah has been identified, we are extremely keen to identify his relatives.
“As part of our efforts so far we have conducted house to house enquiries as well as a witness appeal.
“We want to do everything we can to locate any relatives so that we can speak to them about Mr Obatolah’s death and our ongoing investigation.”
Anyone with information relating to Zodoq Obatolah or his family is urged to contact the IOPC by emailing firstname.lastname@example.org or phoning 03003035592.