  Scalar particles $S$ which are gauge singlets under the Standard Model are
generic features of many models of fundamental physics, in particular as
possible mediators to a hidden or dark sector. We show that the decay $S\to Zh$
provides a powerful probe of the CP nature of the scalar, because it is allowed
only if $S$ has CP-odd interactions. We perform a model-independent analysis of
this decay in the context of an effective Lagrangian and compute the relevant
Wilson coefficients arising from integrating out heavy fermions to one-loop
order. We illustrate our findings with the example of the 750 GeV diphoton
resonance seen by ATLAS and CMS and show that the $S\to Zh$ decay rate could
naturally be of similar magnitude or larger than the diphoton rate.
