The problem of testing treatment difference in the occurrence of a study endpoint in a randomized parallel-group comparative clinical trial with repeated responses under the assumption that the responses follow a bivariate zero-inflated Poisson (ZIP) distribution is considered. Likelihood ratio test for homogeneity of two bivariate ZIP populations is derived. Approximate formula for sample size calculation is also obtained, which achieves a desired power for detecting a clinically meaningful difference under an alternative hypothesis. An example concerning the comparison of treatment effect in an addictive clinical trial in terms of the number of days of illicit drug use during a month is given for illustrative purposes.