A class of tests for the two-sample problem for count data whose test statistic is an
L2-norm of the difference between the empirical probability generating functions associated with each sample is considered. The tests can be applied to count data of any arbitrary fixed dimension. Since the null distribution of the test statistic is unknown, some approximations are investigated. Specifically, the bootstrap, permutation and weighted bootstrap estimators are examined. All of them provide consistent estimators. A simulation study analyzes the performance of these approximations for small and moderate sample sizes. This study also includes a comparison with other two-sample tests whose test statistic is a weighted integral of the difference between the empirical characteristic functions of the samples.