Patrick Fisher (31) died after falling off a balcony at the Waterloo housing block.
Officers went looking for him at the property in Waterloo, following a tip-off from the public regarding his whereabouts, NSW Police said in a statement.
He had two outstanding warrants for assault and stealing.
But the 31-year-old subsequently fell from the balcony and died.
A critical incident investigation has now been launched.
Neighbours and Waterloo residents have expressed their shock and grief following the incident.
More to come...