<p>Two-dimensional (2D) direction-of-arrival (DOA) and polarization parameters play a crucial role in various applications. While many existing 2D DOA estimation methods focus on sparse scalar arrays to enhance degrees-of-freedom (DoFs), there is a growing interest in designing sparse polarimetric arrays and developing corresponding schemes for 2D DOA and polarization estimation. However, the majority of current sparse polarimetric arrays require substantial hardware investments due to considerations such as mutual coupling and antenna array design factors. To address these challenges, we introduce a parallel non-collocated sparse co-centered orthogonal loop and dipole (PNS-COLD) array that offers enhanced DoFs, while maintaining low hardware costs. We then present a polynomial rooting-based closed-form approach for joint 2D DOA and polarization estimation that eliminates the need for spectral searching or pair matching procedures. Our approach utilizes a reconstructed covariance matrix corresponding to the uniform counterpart of the proposed PNS-COLD array, obtained through our proposed submatrix fitting procedure in joint spatial-polarimetric domains. To evaluate the performance of our proposed approach, we derive the Cramér-Rao bound (CRB) for 2D DOA and polarization estimation in underdetermined scenarios. Simulation results are provided to demonstrate the advantages of our proposed approach over some state-of-the-art approaches and the associated CRB.</p>