Scalar particles S that are singlets under the standard model gauge group are generic features of many models of fundamental physics, in particular, as possible mediators to a hidden sector. We show that the decay S→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 using an effective Lagrangian and compute the relevant Wilson coefficients arising from integrating out heavy fermions to one-loop order.