The family found dead at their home in Costessey had recently been in contact with the social services department at Norfolk County Council, it has emerged.
The body of Bartlomiej Kuczynski, 45, was found at his Queen's Hills home alongside his daughters, Jasmin, 12, and Natasha, eight, and his sister-in-law Kanticha Sukpengpanao, 36, last Friday.
Neighbours had said the structural engineer had suffered with mental ill health for several months leading up to the killings and had been seeking help.
The Norfolk and Suffolk NHS Foundation Trust, which provides the region's mental health services, has refused to disclose whether its staff had any dealings with him.
The Norfolk and Norwich University Hospital confirmed that he had been taken to its emergency department by police on December 14, after he had been reported missing.
He then left the unit after he was assessed as having "mental capacity", the hospital said in a statement.
It is now understood that Norfolk County Council's social services department had also had recent contact with the household.
A council spokeswoman said: "As police investigations are at an early stage, it would be inappropriate for us to comment at this time.
"This is such a distressing and sad case and our thoughts are with everyone affected."
The four bodies were discovered by police at a house in Allan Bedford Crescent at around 7.15am on Friday after a 999 call from a dog walker.
Around an hour earlier, Kuczynski had called 999 and said he was "confused" and worried about his mental state, but Norfolk Constabulary did not send officers to the address until the call from the member of the public.
That response to the 999 call is being investigated by the Independent Office for Police Conduct, which is also looking into the December 14 incident, when Kuczynski went missing and was taken to hospital.
It is understood Kuczynski’s wife Nanthaka had left the home on the morning of the deaths to go to work at the Norfolk and Norwich University Hospital. Her sister was visiting the family from Thailand and had been staying at the property for several weeks.
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