In multivariate Statistics you can use Mahalanobis distance to test for multivariate normality. From your post, this is not what you are trying to achieve. Is it?
Given you are talking about 2 groups of data are you looking for a classification process? i.e. use Mahalanobis distance from the centre of each group to potentially re-classify each data point? You can form a classification rule, either linear or otherwise as a classification rule. To proceed you first need to test if Cov(Group A) = Cov(Group B). After this you can decide with rule fits best.