The magnitude and sense of correlation between the inhomogeneous broadening distributions of two neighboring electronic states is shown to have a significant effect on the dispersion of the depolarization ratio, rho, for Raman scattered radiation. To examine this effect quantitatively we treat numerically a model in which two electronic excitations with mutually perpendicular transition dipole orientations are represented by shifted one-dimensional harmonic potentials. The inhomogeneous broadening is treated in the static limit as a Gaussian fluctuation in each of the two electronic origins. The correlation of these shifts is treated as a variable with the fully correlated and fully anti-correlated limits spanning the uncorrelated case. It is shown that the degree of correlation (and its sign) strongly influences the value of the depolarization ratio in some cases which should be amenable to experimental study. Three cases are treated which differ in the separation of the electronic origins of the two states from larger than the total transition width, less than the transition width, and zero. If the state degeneracy is due to symmetry, then in this last case the correlation of the inhomogeneous fluctuations becomes equivalent to symmetric and anti-symmetric environmental variations.