The recently proposed ab initio single-sheeted double many-body expansion potential energy for the methylene molecule has been used to perform quasiclassical trajectory (QCT) calculations for the title reaction. Thermal and initial state-specific (v = 0, j = 0) rate constants for the C(D-1) + H-2/HD/D-2 reactions have been obtained over a wide range of temperatures. Cross sections for the reaction C(D-1) + H-2 and its deuterated isotopes have also been calculated, as well as the CD/CH branching ratios for the C(D-1) + HD reaction. It is found that the CD + H product channel in the C(D-1) + HD reaction is preferred relative to the CH + D channel. The estimated rate constants are predicted to be in the order k(H2) > k(HD) > k(D2) and the calculated cross sections and rate constants compared with available theoretical and experimental data.