The investigation into Surrey County Council upheld 23 complaints about its handling of the family's case including delays in providing appropriate support and the distress caused to the parents when they were left unable to cope.
The LGO report said despite the family first asking the council for help in 2009 with their severely autistic six-year-old son, it took three years for a package of care to be put in place.
Assessments of the child at the time did not properly take into account parental concerns about his violent behaviour on his younger siblings after he had injured them on a number of occasions.
The family reached breaking point after the child's behaviour deteriorated to such an extent that a taxi service refused to take him to school; he frequently wet and soiled himself and his behaviour was described by his paediatrician as "taking the form of sudden, uncontrolled aggression".
The LGO said its findings showed the council had not considered how the child's parents could provide two-to-one care for their son while also working and looking after their other children.
By 2012 they asked the council to find alternative accommodation for their son as they could no longer cope.
However, during an 18-month placement at a specialist children's home the child's parents were notified of 60 incidents including injuries, escapes, and prolonged rages. At one point he was found hanging out of an upstairs window.
It was only after the family threatened the council with legal action in 2013 that it made arrangements to send the child to another specialist unit where his behaviour has subsequently improved.
Ombudsman Michael King said: "This distressing case serves to remind councils of the very real impact on families when councils get things wrong.
"The parents have described the trauma of having to make the decision to seek residential accommodation for their son - a decision they say they would not have made so soon, had they received the support they were entitled to."
A spokesman for Surrey County Council said: "We accept the criticisms in this report and apologise to the family for the impact this must have caused.
"Our involvement with this child started in 2009 and since then a lot of work has been completed to improve our services and to ensure that placement decisions are based on the needs of the child.
"We're confident that this young boy now has the right care in place and are pleased that he is doing well."
Following the LGO investigation, Surrey County Council has agreed to pay the family £13,000 in recognition of the distress caused and the time and trouble taken in bringing the complaint.
