Three-mol % yttria-stabilized tetragonal zirconia poly-crystal (3Y-TZP) is an engineering ceramic utilized for mechanical components and medical implants. We have previously observed fs-laser-induced periodic surface structure (LIPSS) formation on 3Y-TZP and carried out cross-polarized double pulse pair irradiation experiments to investigate formation mechanism. For delay range where the two pulse does not overlap in time domain, the direction of the LIPSS follows the polarization direction of the first arriving pulse. For delay range where the two pulses overlap in time domain, the direction of the LIPSS for 3Y-TZP measured with 20-fs delay step changed from horizontal to vertical with two branches. In this study, we conducted further double-pulse experiments with improved delay resolution of 0.267 fs to investigate the effect of the polarization state of the combined laser pulses on LIPSS formation. Irradiations of cross-polarized double pulse pair and counter-rotating circularly polarized double-pulse pair have been carried out. When the delay was scanned with step of 0.267 fs in the delay range where the pulses overlap in time domain, the direction of the LIPSS on 3Y-TZP changed periodically with delay, which is closely related with the polarization state of the combined laser field. The results are consistent with the dependence of the two branches observed for low delay resolution experiments. Experiments for titanium have been carried out to compare the dependences.