Authorities attended the man's house in Gunnedah, in NSW's northwest, on Friday at 1.40pm after receiving a call with concerns for his welfare.
Assistant Commissioner and Western Region Commander Andrew Holland said the man was killed in a "split-second decision".
Police allege they spoke to the man outside his home before he went back inside and returned with a bow and arrow, forcing them to retreat to their vehicle for cover.
The man then allegedly aimed his weapon at police, prompting them to shoot him.
"These matters, obviously, are split-second decisions by police on the scene," Mr Holland told reporters in Gunnedah on Friday.
"The actions of police will be determined by the critical incident investigation."
The man died at the scene after being treated by paramedics.
A critical incident team from State Crime Command's homicide squad will carry out a critical incident investigation into the man's death, which will be monitored by the Law Enforcement Conduct Commission.
It is at least the third fatality from interactions with police this year.
On January 5, a man suffered a medical episode after he was pepper-sprayed and died in hospital.
He was in the process of being arrested to prevent a "breach of the peace" as police responded to reports of a domestic violence incident in Sydney's inner west.
On January 8, police shot dead a man who was believed to have been experiencing a mental health episode when he barricaded himself inside a house during a six-hour stand-off.
The 49-year-old reportedly armed himself with a shard of glass and had taken hold of an officer before they shot him.
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