Hmm...  I actually am not entirely sure either.  Its just that
the Crane is a favored animal in Japan, and one that is linked
with marriage, to my knowledge.  Cranes mate for life, and when
one mate dies, the other will pine away until it dies.  I suppose
if they don't believe in afterlife, its a moot point, but I was
under the impression that they took marriage as something which
transcended life and death.

They do. The Japanese do believe in an afterlife, The Shinto priests,
however, do not teach about these matters. That is the task of the
Buddhist priests. 
Lt. Trakal
GP No Tantei-A