A critical incident has been declared in Sydney after a man died after falling from a unit balcony while he was being pursued by police.

Authorities claim that the man used a knife to rob a local grocery store in a “frightening” encounter before he fell off a building in Surry Hills around 9:10 pm last night.

CCTV from a shop on the next street shows a man in a mask wielding a large knife.

Police headed to the apartments in Belvoir St an hour later as part of their investigations.

A man and woman were in the hallway of the units when police arrived, with police saying he ran when he saw officers.

“When police approached the residence, a man, believed to be in his 40s, fled the apartment complex, leaped over a balcony, and tragically fell five stories to his death,” Acting Assistant Commissioner Scott Tanner reported.

Police gave the man first aid until paramedics arrived.

He was rushed to hospital but died on the way.

Police also arrested a 21-year-old woman who allegedly closed the unit door on officers after the man ran from police.

She has been charged with offences including robbery.

She’s due in court today.

Both the man and women are well known to police.

A critical incident team from Inner West Police Area Command will investigate the circumstances surrounding the incident.

An independent review will be conducted on the investigation by the Professional Standards Command with oversight from the Law Enforcement Conduct Commission.

A report will be prepared for the Coroner.