In this paper we consider a duopoly model of multidimensional vertical product differentiation where product features are discrete and consumers' tastes are described by a joint density function that belongs to the class of Elliptically Contoured Distributions. We prove that in any equilibrium one firm always includes all characteristics in the product. Moreover, when types have perfect positive correlation the unique equilibrium involves maximum differentiation. More importantly, the main result states that the other firm's equilibrium level of differentiation is determined by the correlation among types.