We study 416 galaxy systems with more than 7 members selected from the 2MASS catalog. We applied five well known normality tests to the velocity distributions of these systems to distinguish Gaussian and non-Gaussian clusters. Using controlled samples, we estimated type I and II errors for each test. We verified that individual tests minimize the chances of classifying a Gaussian system as non-Gaussian, while the Fisher's meta-analysis method, a procedure to combine p-values from several statistical tests, minimizes the chances of classifying a non-Gaussian system as Gaussian. Taking the positive elements of each method and also including a modality analysis of the velocity distribution, we defined objective criteria to split up the sample into Gaussian and non-Gaussian clusters. Our analysis indicates that 50-58% of groups have Gaussian distribution, a lower fraction than that we found using individual normality tests, 71-87%. We also found that some properties of galaxy clusters are significantly different between Gaussian and non-Gaussian systems. For instance, non-Gaussian clusters have larger radii and contain more galaxies than Gaussian clusters. Finally, we discussed the importance of choosing the adequate methodology to classify galaxy systems from their velocity distributions and also the dependence of the results on the criteria used to identify clusters in galaxy surveys.