13-year-old said to have shot his police officer parents, grandmother and aunt before turning gun on himself

São Paulo police have said that Marcelo Pesseghini was a "sweet child". They are mystified as to why on Sunday evening the 13-year-old pupil seemingly murdered his police officer parents, his grandmother and his aunt before shooting himself.

Three of the victims were apparently sleeping in the family home in Brasilândia, north São Paulo, when they were killed. The body of his mother, Andreia, 36, was found slumped on her knees beside a bed, her arms covering her head. All were killed with a police-issue revolver, discovered in the dead teenager's hand.

Police investigating the murder believe the boy killed all four family members on Sunday night, then drove his mother's car to school, arriving at 1.25am on Monday. At 6.23am security cameras captured a boy identified as him with a rucksack getting out of the car and entering the school. The father of a school friend then gave him a lift home.

But on Wednesday the police colonel in charge of the unit where Marcelo's mother was a corporal questioned the official account and said she recently denounced colleagues for robbing cash machines. Police Colonel Wagner Dimas told São Paulo's Rádio Bandeirantes he did not believe the official version of events. "Today I am not convinced," Dimas said.

Marcelo had no history of violence, police say, but was obsessed with weapons and had a large collection of toy guns and a protective breastplate made of cardboard in his bedroom, police said.

Detective Itagiba Franco, who is investigating the case, told the Guardian that in 37 years in the force he had not seen a case like it. "We interviewed a friend of his at school, who said Marcelo's dream had been to be a hired killer and that he wanted to kill his parents at night and live in an abandoned house," Franco said. He added that there was no evidence anyone had invaded the house nor that the crime was linked to his parents' police work. "This is not a usual murder."

Dimas told the radio station that Marcelo's mother recently denounced fellow officers for robbing cash machines and although some officers were transferred following an investigation nobody was punished. "The problem with investigations is to reach a conclusion. We did not reach a conclusion," he said.

Dimas said he had no knowledge of Andreia Pesseghini being threatened and that time would tell what had really happened. "Let's see if there is any reason in this puzzle here," he said.

Police said they knew nothing of allegations by Andreia Pesseghini but would investigate Dimas's claim.

The Pesseghini family massacre has appalled Brazil – a nation hardened by soaring homicide rates. Rights groups estimate as many as 60,000 Brazilians are murdered each year.

Marcelo's father, Luís, 40, had been a member of São Paulo's police for 18 years. He graduated to the role of sergeant in the force's elite Rota unit – an armed Swat team employed for rapid response.

In 2011, Rota was involved in at least two cases in which suspected criminals were allegedly murdered by police. In May 2012, six people believed to have been members of armed criminal gang were killed in a confrontation with the unit. Hundreds of civilians and police were killed in a wave of violence in subsequent months that terrorised the city.

Marcelo's mother was also a long-serving police officer, working in administration. His grandmother Benedita, 65, and an aunt, Bernadete Silva, 55, were found dead in a separate house on the same property.