We propose a method for prediction using spatial count data that can be reasonably modeled assuming the Conway-Maxwell Poisson distribution. We develop the Conway Maxwell-Poisson model (COM-Poisson), which is a two parameter generalisation of the Poisson distribution. The COM-Poisson distribution allows for the flexibility needed to model count data that are either over or under-dispersed. The limiting factor of the COM-Poisson distribution is that the likelihood function contains multiple intractable normalizing constants and is not always feasible for MCMC techniques. Also, allowing for spatial random effect induces additional variability that makes it unclear if the spatial Conway-Maxwell random variable is over or under dispersed. We propose a computationally efficient hierarchical Bayesian model that addresses these issues. We demonstrate the wide applicability of our approach using a simulation study, and an application using voting data obtained from the Florida Division of Elections.