Polarizabilities calculated for sexithiophene using Hartree-Fock and density-functional approaches with a 6-31G* basis set are used to calculate refractive indices and local electric field tensors in the alpha -sexithiophene crystal. The calculations under-estimate the (incomplete) experimental refractive indices but polarizabilities are devised that fit them. These predict that the unknown refractive index perpendicular to the crystal be plane is larger than those in the plane. The tilted molecular long axis produces sizeable off-diagonal local-field components in the crystal ac plane. This complicates the analysis of electro-absorption spectroscopy.