Two other kids suffered minor injuries, and the 2-year-old remains in critical condition.
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This week's heatwave is a factor as tree roots suck up more groundwater, according to local arborists.
"The water being carried to the end of the branches to keep the leaves hydrated create weight and if there's a structural defect in that tree, it can fail," said arborist Rebecca Latta.
Latta is an arborist who used to work as Pasadena's City Forester.
The tree that fell is a Eucalyptus, known to lose limbs in hot weather. Latta said Eucalyptus and other large trees scattered across the Los Angeles area need to be maintained and inspected on a regular basis.
"Most local cities need to increase their inspection budgets," said Latta. "You can't predict every failure, but you can see a lot of things with experienced eyes."
Pasadena has seen similar tree dangers recently.
Earlier this month, a tree came crashing down at Villa Park, narrowly missing several soccer players sitting on a nearby bench. And two years ago, a tree toppled near the Pasadena Kidspace Museum, injuring eight kids, two of them critically.
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A spokesman for the city of Pasadena said that the cause of the accident Tuesday is still under investigation.
The latest fallen tree, however, has sparked a lot of finger pointing.
The Pasadena Unified School District leases the former school to a private daycare center and the LAND to the city for use as a park.
The Pasadena city spokesman said that means the school district is responsible for taking care of the trees.
The School District spokesperson says it's the city's responsibility.
Residents just want to make sure their trees are safe and plentiful.