We investigated the Stark effect on centrosymmetric dibenzanthanthrene molecules in naphthalene, a centrosymmetric crystal, where it is mainly quadratic, and in the Shpol'skii matrix hexadecane, where we found linear and quadratic contributions. The molecules with large linear coefficients are dominantly found in the wings of the main site. The distribution of linear coefficients points to two populations of molecules, one of them in a centrosymmetric environment, the other one centrosymmetric on average, but very sensitive to, or located near, crystal defects. The distributions of quadratic coefficients in both systems is attributed to orientational disorder. We discuss the case of a molecule with higher-order terms in its Stark shift, and attribute it to geometrical changes of the supermolecule in the applied electric field.