Police have shot dead a man on the New South Wales Central Coast, prompting a critical incident investigation.

It is understood officers were called to a home on Bangalow Street in Ettalong Beach after reports of a domestic dispute about 8.30am on Sunday.

A 45-year-old man was shot in the chest after a confrontation with officers.

He was treated by paramedics at the scene and taken to Gosford Hospital in a critical condition, but he died a short time later.

NSW Police Commissioner Andrew Scipione said there would be a full investigation.

"A crime scene has been established and further details are expected later today," he said.

A critical incident team from the homicide squad is investigating all the circumstances around the incident.

Critical incident investigations are called when police may be involved in a death.

The investigation will be overseen by the police Professional Standards Command.