  In this paper, we prove that the generalized Br\'ezin-Gross-Witten
tau-function is a hypergeometric solution of the BKP hierarchy with simple
weight generating function. We claim that it describes a spin version of the
strictly monotone Hurwitz numbers. A family of the hypergeometric tau-functions
of the BKP hierarchy, corresponding to the rational weight generating
functions, is investigated. In particular, the cut-and-join operators are
constructed, and the explicit description of the BKP Sato Grassmannian points
is derived. Representatives of this family can be associated with interesting
families of spin Hurwitz numbers including a spin version of the monotone
Hurwitz numbers.
