Let E be an elliptic curve defined over Q. Suppose it has complex multiplication by an order of an imaginary quadratic extension K/Q and p is a prime of good ordinary reduction. Also, suppose that the sign of functional equation of L(E,s) is -1 and p splits in K. Accordingly, the anticyclotomic Katz p-adic L-function vanishes. Is there a version of p-adic Gross - Zagier formula for the two variable Katz p-adic L-function in this case? The results of Perrin - Riou seem to exclude this choice of imaginary quadratic extension.