Through genome-wide association studies, numerous genes have been shown to be associated with multiple phenotypes. To determine the overlap of genetic susceptibility of correlated phenotypes, one can apply multivariate regression or dimension reduction techniques, such as principal components analysis, and test for the association with the principal components of the phenotypes rather than the individual phenotypes. However, as these approaches test whether there is a genetic effect for at least one of the phenotypes, a significant test result does not necessarily imply pleiotropy. Recently, a method called Pleiotropy Estimation and Test Bootstrap (PET-B) has been proposed to specifically test for pleiotropy (i.e., that two normally distributed phenotypes are both associated with the single nucleotide polymorphism of interest). Although the method examines the genetic overlap between the two quantitative phenotypes, the extension to binary phenotypes, three or more phenotypes, and rare variants is not straightforward. We provide two approaches to formally test this pleiotropic relationship in multiple scenarios. These approaches depend on permuting the phenotypes of interest and comparing the set of observed P-values to the set of permuted P-values in relation to the origin (e.g., a vector of zeros) either using the Hausdorff metric or a cutoff-based approach. These approaches are appropriate for categorical and quantitative phenotypes, more than two phenotypes, common variants and rare variants. We evaluate these approaches under various simulation scenarios and apply them to the COPDGene study, a case-control study of chronic obstructive pulmonary disease in current and former smokers.