In this article, we experimentally and numerically investigated a metamaterial (MM) geometry capable of exhibiting polarization independent double-band electromagnetic induced transparency (EIT) effect. The meta-molecule unit of the proposed MM configuration composed of a strip and two asymmetric split ring resonators (SRRs). For polarization independent doubleband EIT effect, the existing meta-molecule unit is converted into a cross-like structure adorned with four SRRs. Terahertz transmission response is analyzed for two orthogonal polarization directions of the incident light to confirm the polarization independent response. In order to understand and explain our numerical findings more elaborately we have employed four-level tripod atomic system based analytical model. The transmission response is also analyzed for different angle of incidence of the two orthogonal polarizations. In order to demonstrate the practical applicability of our study, we have studied the effect of transmission with the change of refractive index of analyte of thickness 10 μm coated on the top of the MM resonators. The calculated sensitivities for the 1st, 2nd and 3rd dips are 121 GHz/RIU, 138 GHz/RIU and 135 GHz/RIU (RIU, refractive index unit) respectively. Our study can also play an important role in the advancement of slow light devices, modulators and filters.