6:25 PM PT — David shared a photo of Kate, whom he calls "Katy," at his book signing … along with a heartfelt and encouraging message.
David Spade leaned on a friend hours after getting the tragic news about sister-in-law Kate Spade's death.
The actor and comedian was out in L.A. Tuesday afternoon, looking solemn as he left home. His brother, Andy, was married to Kate and … as we reported, he was home when she hanged herself.
David wore sunglasses and kept his head down, but was seen getting a consoling hug from a friend.
Kate and David's bro launched Kate Spade Handbags together in 1993 and got married in 1994. They have a daughter together — 13-year-old Frances Beatrix.
We broke the story … Kate left a suicide note behind addressed directly to Frances that said, "Bea – I have always loved you. This is not your fault. Ask Daddy!"
Kate was 55.