The isotopic product CD/CH branching ratios, thermal rate coefficients, as well as other dynamical quantities of the C(¹D) + HD → CD(H) + H(D) reaction are investigated by detailed quasiclassical trajectory calculations on the highly accurate singlet ground-state (ã¹A′) and the first excited-state (¹A′′) global ab initio potential energy surfaces (PESs) recently constructed by us. The calculated CD/CH branching ratios are in reasonable agreement with experiment. The thermal rate coefficients in the temperature range of 200–1500 K are calculated, and the obtained values at room temperature are in very good agreement with available experimental data. The distinct topographical features between the present and previous PESs, which influence the CD/CH branching ratio, are also discussed. In addition, the effect of the ¹A′′ PES is investigated, and the results show that the contribution from the ¹A′′ PES to the total reactivity is rather noticeable.