  We study the CP violating ZZZ vertex in the two-Higgs doublet model, which is
a probe of a Jarlskog-type invariant in the extended Higgs sector. The form
factor $f_4^Z$ is evaluated at one loop in a general $R_\xi$ gauge and its
magnitude is estimated in the realistic parameter space. Then we turn to the
decoupling limit of the two-Higgs doublet model, where the extra scalars are
heavy and the physics can be described by the Standard Model supplemented by
higher-dimensional operators. The leading operator contributing to $f_4^Z$ at
one loop is identified. The CP violating ZZZ vertex is not generated in the
effective theory by dimension-8 operators, but instead arises only at the
dimension-12 level, which implies an additional suppression by powers of the
heavy Higgs mass scale.
