12:30 PM PT -- Our law enforcement sources confirm Kate's husband, Andy was home at the time she died.

11:45 AM PT -- Our law enforcement sources confirm the note Kate left behind was addressed to her daughter ... telling the 13-year-old the suicide wasn't her fault.

Iconic fashion designer Kate Spade was found dead of an apparent suicide Tuesday morning in her NYC apartment ... TMZ has learned.

Law enforcement sources confirm a housekeeper found Kate's body at 10:20 AM ET in her Park Avenue home. We're told she hanged herself using a scarf tied to her bedroom door knob. She was pronounced dead on the scene. We're also told she left a note.

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Kate got her start in the '80s working for women's magazine "Mademoiselle" in Manhattan, when she moved in with Andy Spade -- David Spade's brother. She and Andy met while attending Arizona State University and working at a clothing store.

Together, they launched Kate Spade Handbags in 1993, and it blossomed into a full-scale clothing and jewelry line. Kate and Andy got married in 1994.

Kate sold her company in 2007 and took some time off to raise her daughter -- but got back in the game in 2016 by launching a new fashion brand called Frances Valentine ... named after her daughter, who's now 13 years old.

Kate was 55.