A man has been shot dead by police after a woman was stabbed in a rampage that saw him allegedly break into several houses and carjack a vehicle. The man reportedly forced his way into the woman's house armed with a chainsaw and knife on Friday morning, February 6. A critical incident investigation is underway after the series of events unfolded in the early hours in New South Wales in Australia . Police officers were called to a home on Heath Avenue, Tuncurry, just over three hours from Sydney