Police investigating the deaths of three women and the man who shot them before killing himself are expected to focus on why he owned six guns.
Michael Atherton, 42, had licences for the firearms despite police revealing they were told three years ago that he had threatened to harm himself.
He shot his partner Susan McGoldrick, her sister Alison Turnbull, 44, and her niece Tanya Turnbull, 24.
Officers found the bodies inside the house in Horden, Co Durham, on Sunday.
Det Supt Paul Goundry said detectives were not looking for anyone else in connection with the deaths of 47-year-old Ms McGoldrick and the two other women.
Three other people managed to escape, including a 19-year-old woman named locally as Laura McGoldrick who escaped from an upstairs window of the building in Greenside Avenue and is believed to have suffered minor injuries.
Police found the victims downstairs in different rooms of the house in Horden near Peterlee.
Assistant Chief Constable Michael Banks said Mr Atherton was licensed to own six weapons, three of them shotguns and a further three "section-one" firearms.
The latter required a greater degree of authorisation than a shotgun licence, he said.
Mr Atherton had been a member of a gun club in the area but it is not known if he was still an active member.
"I can confirm that a resident at that address was the lawful holder of shotgun and firearms licences and we cannot confirm at this stage whether any of those weapons that were lawfully held have been used in this," said Mr Banks.
It has also emerged that the Durham force had previously had what has been described as "minor contact" with the family and that as a result, a voluntary referral to the Independent Police Complaints Commission (IPCC) was being made.
The victims had been in a group celebrating the new year in what police have called a "close and very settled community".
Mr Goundry, who described the deaths as "a tragic event", added: "We have four people who died and our thoughts and feelings are with their family and friends at this moment."
Easington Labour MP Grahame Morris described the area as a "very tight-knit former mining community" and said it had been very traumatic for everyone.
He said: "There are a number of big questions that are being raised about the consequences of keeping firearms at home and whether an individual's mental state should be a determining factor in issuing firearms certificates.
"It's easy with the benefit of hindsight of course to be wise after the event but the police have referred the matter to the IPCC who are also going to investigate the matter and hopefully will come forward with some recommendations."
Shooting organisation the British Association for Shooting and Conservation expressed sympathy for the victims' families but warned against any kneejerk reaction.
It said: "There has just been a comprehensive parliamentary review of firearms law in the UK and the facts in this incident need to be firmly established."