Biomedical count data such as the number of seizures for epilepsy patients, number of swollen or tender joints observed for the rheumatoid arthritis patients are common. Often these counts are longitudinally measured from patients within clusters in multisite trials. The Poisson and negative binomial models are not adequate when data exhibit over and under-dispersion, respectively. We propose the Conway-Maxwell Poisson (CMP) regression model to overcome this difficulty as it can capture a wide range of dispersion. Specifically, we develop a regression model with random intercept and slope to capture subject or cluster specific heterogeneity. Adding more random effects makes CMP mixed model complicated as the random effects are to be integrated out during estimation, especially in classical setting. In this regard, we apply an adaptive variant of Hamiltonian MCMC to carry out Bayesian computation. We then use Deviance Information Criterion (DIC) for model comparison. A case study demonstrating the usefulness of the proposed methodology is applied using biomedical data.