Wertheim's multidensity formalism for pairwise additive molecular interaction is extended to handle nonadditive contributions and is applied to formulate an equation of state (WEOS) for the Gaussian-charge polarizable model (GCPM) of water, with cluster integrals appearing in the theory calculated via the Mayer sampling Monte Carlo method. At both sub- and supercritical temperatures, the equation of state of GCPM water obtained from WEOS converges well to Monte Carlo simulation data, and performs significantly better than the conventional virial treatment (VEOS). The critical temperature for GCPM water using a fourth-order WEOS is given to within 1.3% of the established value, compared to a 17% error shown by fifth-order VEOS; as seen in previous applications, the critical density obtained from both VEOS and WEOS significantly underestimates the true critical density for GCPM water. Examination of the magnitudes of the computed cluster diagrams at the critical density finds that negligible contributions are made by clusters in which a water molecule has both of its hydrogens involved in association interactions.