Recent solid-state experiments manage to create a two-dimensional system of excitons created from electrons and holes confined in double quantum wells structure. In such a system, we study the short-range behavior which is the behavior of the system when two excitons become close to each other. To this end, we utilize the contact formalism devised recently by Tan to study the universal properties of this system. Specifically, we present our results regarding one-body and two-body momentum distribution and the spectral function of the system.