A large gum tree that fell and killed a toddler in the Dandenong Ranges at the weekend was on land the local Yarra Ranges Council "had care and management responsibilities", its environment and engineering director Mark Varmalis said.

The tragedy has prompted criticism that local governments across the state are not spending enough time and money checking for hazardous trees, which often do not show any obvious danger signs.

The Municipal Association of Victoria agrees there is a "funding issue", but said councils and the state government first needed to establish best-practice guidelines on tree management before committing more money.

Two-year-old Eli Marnock died on Saturday night when a 30-metre tree crashed into his bedroom during wild weather. His five-year-old sister Nicola, who had been on the couch in the living room, was also badly injured when she was pinned under the collapsed house.

On Monday Yarra Ranges Council's environment and engineering director Mark Varmalis confirmed the deadly tree was under their care. However the council could find no evidence to back up claims made by residents that they had been previously asked to cut down the tree.

"We can … confirm that from investigation of our customer request systems, that the council had not received any requests or complaints regarding that tree," Mr Varmalis said.

Despite common misconceptions, dangerous trees can be extremely difficult to identify. Melbourne University arboriculture expert Greg Moore said most symptoms of ill-health took place below the ground, requiring experts sometimes with sophisticated technology to diagnose the problem.

Dr Moore said although most councils had good tree inspection policies, their teams of arborists were often forced to work with very limited budgets. He said local governments would generally allocate $10 to $20 on average for the care of each tree in their municipality, but it costs $300 to $500 for a proper tree inspection.

"[The] best thing you can do is identify a small number of potential trees [likely to be a potential danger]," he said. Dr Moore added that smaller rural and regional councils had less money to spend to care for a large number of trees.

The Yarra Ranges Council "actively manages" more than 5 million trees within the municipality, with an annual budget of about $3.5 million.

MAV chief executive Rob Spence said the peak council body would seek talks with the state government about establishing "appropriate" tree inspection standards.

He said management of trees was an enormous task for councils, particularly in regions like the Dandenongs, where there were large numbers of trees, and passion for their preservation.

Meanwhile, he said councils received a number of complaints about healthy trees people wanted removed for other reasons, including obscuring their view.

Eli's family shared fond memories of the toddler on Monday, describing him as "the bee's knees".

"You couldn't look at him and not smile at him…[he] made everybody laugh," his aunt, Sharon Surridge, told Channel 10 news.

Grandfather John Surridge told the station the family moved to the Dandenong Ranges to be amongst the trees.

"We only had him for a short time but the memories were fantastic," Mr Surridge said.

On Monday the state government would not provide any more details on an earlier pledge to review the "processes" around tree management.

"This incident remains under investigation and it's appropriate that those inquiries are resolved before providing further comment," local government minister Natalie Hutchins said.

"While I won't be commenting on specific incidents, the weekend's severe weather is a reminder for all councils to ensure their maintenance systems are in check and that they are fully aware of their responsibilities when it comes to the safety of local residents."