Authorities attended the man's house in Gunnedah, in NSW's west, on Friday at 1.40pm after receiving a call with concerns for his welfare.
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.
Paramedics treated him but the man was dead.
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 who 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.
Police will carry out a critical incident investigation into the Gunnedah death, which will be monitored by the Law Enforcement Conduct Commission.
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