The stereodynamics of the O(D-1) + HD(v = 0,j = 0) reaction has been studied theoretically on the Dobbyn-Knowles (DK) ab initio potential energy surfaces (PES). Quasiclassical trajectory (QCT) calculations have been carried out on the 1 (1)A' ground state PES and both QCT and quantum mechanical (QM) calculations have been performed on the 1 (1)A " excited state PES. The product rotational angular momentum (j') polarization in the (k,k') scattering frame (i.e., the k-k'-j' vector correlation) has been determined for selected rovibrational states of the OH(v',j') + D and OD(v',j') + H product channels at the collision energy of 0.196 eV. The agreement between the QM and QCT results is very good and indicates that the "abstraction" reaction occurring on the excited 1 (1)A " PES yields OH and OD products strongly polarized, in strong contract with the "insertion" reaction occurring on the ground 1 (1)A' PES, which leads to an essentially isotropic distribution of the product rotational angular momentum. The differentiated stereodynamics on the 1 (1)A' and 1 (1)A " surfaces constitutes a reference for experimental research with the aim of assessing the contribution of the excited 1 (1)A " surface to the overall reactivity of this system.