No injuries were reported in the incident, which occurred about 2:30 a.m. near the intersection of Neenach Street and Telfair Avenue, just north of the 5 Freeway.
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On Monday morning, city crews were using chainsaws and other equipment to cut up the part of the tree that fell and remove it from the property.
Resident Maura Taura said that although the toppled tree came close to the house, she was grateful that the home was not damaged.
Taura told ABC7 that her daughter sleeps in a bedroom with her two children that is located just feet away from where the tree came down.
Taura said the giant tree had previously been a cause of concern, especially when large branches fell off in the past. She recalled an incident about a year ago when a branch fell onto her son's truck.
Los Angeles City Councilwoman Imelda Padilla visited the scene on Monday and spoke with residents of the neighborhood who reiterated their concerns.
Tropical Storm Hilary prompts school closures throughout SoCal
Elsewhere in Sun Valley on Sunday, Los Angeles Fire Chief Kristin Crowley, the Fire Department responded after five vehicles became stranded amid Hilary's torrential rains. Firefighters rescued one person from one of the vehicles; no other entrapments were reported.
Tropical Storm Hilary first made landfall in Baja California on Sunday in a sparsely populated area about 150 miles south of Ensenada. One person drowned. It then moved through mudslide-prone Tijuana, threatening the improvised homes that cling to hillsides just south of the U.S. border.
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The National Hurricane Center in Miami downgraded Hilary to a post-tropical storm Monday morning, but warned that "continued life-threatening and locally catastrophic flooding" was expected over portions of the southwestern U.S., along with record-breaking rainfall.
The Associated Press contributed to this report.