A study of the effect of an external electric field on spectral holes burnt at different frequencies in the inhomogeneous absorption band of a centrosymmetric squaraine dye, bis [4-(diethylamino)-2-hydroxyphenyl] squaraine (DEAH), in polymers of different polarity is presented. Average matrix induced dipole moment differences of about 1 D and 0.37 D were measured in the directions parallel and perpendicular to the long axis of DEAH. In all polymers investigated, the induced dipole moment difference decreased from the higher to the lower frequencies. Solvatochromic shift measurements were performed in order to elucidate the origin of this effect. The matrix field inducing the dipole moment is also partially responsible for the frequency shift of the absorption of DEAH. With increasing matrix field, the absorptiion frequency is shifted to the blue due to electrostatic interaction with the local dipoles of DEAH. The contribution of the electrostatic interactions to the frequency shift is smaller than the dispersion interactions by two orders of magnitude in polystyrene, but increases slightly in more polar polymers.