The blaze broke out after 9 p.m. Wednesday.
A large portion of the roof collapsed at the building in the unit block of Billie Ellis Lane before firefighters gained the upper hand.
Authorities confirmed Thursday morning that a 73-year-old woman, identified as Larisa Bartrone, was found dead inside.
Another 35 residents have been displaced.
Fire investigators are working to determine what sparked the blaze.
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