Results reported in this paper on the electro-optic properties and dielectric relaxation in the SMCA* and SmC* phase of a liquid material as a function of sample thickness. The measurements were carried out in 3 mum, 6 mum, and 10 mum thick cells. In the whole SmC* phase two modes were obtained in the low frequency region of the dielectric spectra in each of the three cells without bias electric field. The relaxation strength of both the modes sharply decreases with the applied bias dc electric field. One of the modes is assigned as Goldstone mode, arises due to phase fluctuation and the origin of the other mode may be related to the space charge accumulated at the interface between liquid crystal and the polymer coating. In antiferroelectric liquid crystal (SMCA*) phase two switching current peaks were observed only in a 3 mum thick cell by applying triangular wave of frequency around 30 Hz-40 Hz. Two antiferroelectric modes were obtained in the dielectric spectra of SMCA* phase in the low frequency region and the results have been dicussed. Both the results of spontaneous polarization and dielectric studies reveal that the antiferroelectric behavior in the SMCA* phase is squeezed in each of the three cells.