Ruan (2015) recently proposed using a finite mixture model with components modelled by Gaussian copula with Poisson margins (BP-GCD) as the basis for model-based clustering of bivariate correlated counts. Although the Poisson distribution is a useful model for modelling count data, the distribution is constrained by its equi-dispersion assumption. Motivated by this limitation, the thesis introduces a more flexible model, one with Gaussian copula models as components but with Conway-Maxwell Poisson (COM-Poisson) margins (BCOM-GCD) which allows the accounting of under- and over-dispersion in the correlated count data. We test our proposed method on a variety of simulated settings and on data from the Australian National Health Survey to explore the impact of ignoring the non-equidispersion. Our simulations and real-life data analysis indicate that using BCOM-GCDs as mixture components instead of BP-GCDs provides a better and more flexible approach for performing model-based clustering for under- or over-dispersed counts.