A man has been arrested during an investigation into a deadly police shooting on the New South Wales Central Coast.

Police shot dead a 37-year-old man at Hamlyn Terrace after he allegedly pointed a double-barrelled firearm at them last Thursday morning.

The man had been attempting to break into an outbuilding at a rural property in Hamlyn Terrace, near Wyong, at around 10am that day when police caught up to him.

Earlier, a police chase was sparked by a call from a member of the public, who had been chasing a stolen Toyota Land Cruiser driven by the man just before 10am.

A police pursuit ensued and with the help of PolAir, the stolen Land Cruiser was spotted outside the Minnesota Road property.

The man's gun had been lying on the ground beside him but when called on by police, he picked up the weapon and aimed it at the officers, according to NSW Police's Assistant Commissioner Max Mitchell.

The assistant commissioner backed the conduct of the officers involved, saying they have his "full support".

"My view is very clear: the police have acted professionally," he said.

A critical incident investigation into the shooting is underway.

A 46-year-man on a number of outstanding warrants was arrested in Springfield yesterday evening in connection with the investigation.

He was charged with domestic violence offences.

Police believe he was with the armed man at some point on the day of the shooting.

Source: 9News https://www.9news.com.au/national/central-coast-police-shooting-man-arrested-in-springfield-nsw/a76316b5-dbdd-4f80-88e2-d9f9fbadc9aa