We present an in-depth theoretical study of the C(D-1) + HD v = 0, j = 0) -> CD (CH) (v', j') + H (D) reaction using a time-dependent wave packet method with full Coriolis coupling on the Zhang-Ma-Bian potential energy surfaces (PESs) recently constructed by our group. The integral cross sections (ICS), differential cross sections, CD/CH branching ratios, and product state distributions are calculated over a wide range of collision energies. We find that the vibrational branching ratio defined as ICS(v'=I)/ICS(v'=0) obtained from the (b) over tilde (1)A '' PES is much smaller than that from the (a) over tilde (1)A' PES for both product channels, which may be attributed to the dynamical effects of the conical intersection regulated (CI-R) intermediate on the (b) over tilde (1)A '' PES. The collision energy dependence of CD/CH branching ratios displays oscillatory structures, which may be caused by the resonance states supported by the wells on the PESs. The high-temperature rate coefficients are also obtained and compared with previous results. The role of the excited state PESs is also discussed.