All the neighbors are gathering together all the evidence to bring together all the mysterious events that led to the shocking moment when a mother from Melbourne is believed to have killed her three children and then, herself.

The bodies of Katie Perinovic, her two daughters Claire, 7, Anna, 5, and son Matthew, 3, were discovered inside their home in Tullamarine, on the northern outskirts of the city, on Thursday afternoon.

Perinovic's husband, Tomislav, 48, was the first to find the bodies of his three children and his wife and immediately called emergency services. After being questioned by police, he was released without charge.

Less than 24 hours before the shocking killings, 42-year-old Perinovic had sent a bag of plums to her neighbors' house on Burgess Street, to neighbors Daniel and Vicky Schembri.

Mr Schembri, who has lived on the same street with the Perinovic family for 48 years, said Katie knocked on his door at 5.30pm on Wednesday.

He thanked her for the plums, and she said "Goodbye." Just two days ago, Schembri also confessed that he had seen three children playing happily in the pool of their house: "They played happy and looked very happy" - he told "The Australian".