  A characterization of the Kadomtsev-Petviashvili hierarchy of type C (CKP) in
terms of the KP tau-function is given. Namely, we prove that the CKP hierarchy
can be identified with the restriction of odd times flows of the KP hierarchy
on the locus of turning points of the second flow. The notion of CKP
tau-function is clarified and connected with the KP tau function.
Algebraic-geometrical solutions and in particular elliptic solutions are
discussed in detail. The new identity for theta-functions of curves with
holomorphic involution having fixed points is obtained.
