Yuma clearly remembered the significance that the Book of Death and Shinigami personally had to him in some way. He could've entrusted it to Makoto, who lives in and has access to the most secure places in Kanai Ward, and already had a comfortable knowledge about the book even without any memory of the Mystery Labyrinth.
He could've given it to Vivia, who is not only an incredibly capable detective and a book enthusiast who would probably store it safely, but also his insane forte giving him the ability to actually see Shinigami and remember the Mystery Labyrinth without a pact makes him one of the most knowledgeable people about the Book of Death probably ever. On top of that, he's definitely way too lazy and unmotivated to abuse it in any way.
But he gave it to Kurumi. Someone who is (homunculus status notwithstanding) essentially an average girl who probably knows nothing about the book unless on the off-chance that Vivia or Makoto filled her in. There's really no pragmatic reason to give it to her.
Yuma gave it to her, because it's his roundabout way of saying that she's where he intends to return to.
Or maybe even, he anticipated that she's the type of person who could find her way to him, since the condition he had set for coming back is an inherently impossible task. In a way, isn't that entrusting another person with something that you wouldn't be able to do on your own?
