When overdispersion is present in count data, a negative binomial (NB) model is commonly used in place of the standard Poisson model. However, the model is sometimes not adequate because of the occurrence of excess zeros and a zero-inflated negative binomial (ZNB) model may be more appropriate. This article proposes a general score test statistic for comparing a ZNB regression model to the NB model and the test is extended to a composite score test. Simulation results indicate that the test performs reasonably well and has a sampling distribution under the null hypothesis (NB model) approximated by the usual 2 distribution. Use of the test is illustrated on a set of apple shoot propagation data. The composite score test is found to indicate suitable models.