  In models with extended scalar sectors with several Higgs multiplets, such as
Higgs triplet models, the $Z$ gauge boson can have nondiagonal couplings to
charged Higgs bosons. In a model-independent way, we study the potential
contributions arising from such theories to the CP-violating trilinear neutral
gauge boson couplings $ZZ^*\gamma$, $ZZ\gamma^*$, and $ZZZ^*$, which are
parametrized by four form factors: $h^Z_{1,2}$, $f_4^\gamma$, and $f_4^Z$,
respectively. Such form factors can only be induced if there are at least two
nondegenerate charged Higgs scalars and an imaginary phase in the coupling
constants. For the masses of the charged scalar bosons we consider values above
300 GeV and find that the form factors can reach the following orders of
magnitude: $|h_1^Z|\sim 10^{-5}-10^{-4}$, $|h_2^Z|\sim 10^{-7}-10^{-6}$,
$|f_4^\gamma|\sim 10^{-5}-10^{-3}$ and $|f_4^Z|\sim 10^{-6}-10^{-5}$, though
there could be an additional suppression factor arising from the coupling
constants. We also find that the form factors decouple at high energies and are
not very sensitive to a change in the masses of the charged scalar bosons.
Apart from a proportionality factor, our results for the $f_4^Z$ form factor,
associated with the $ZZZ^*$ vertex, is of the same order of magnitude than that
induced via nondiagonal neutral scalar boson couplings in the framework of a
two-Higgs doublet model.
