We present the Born-Oppenheimer coupled-channel dynamics of the reaction (12)C((1)D)+(1)H(2)(X (1)Sigma(g) (+))-->CH(X (2)Pi)+H((2)S), considering the uncoupled CH(2) states ã (1)A(1) and b (1)B(1), the permutation-inversion symmetry, and Coriolis interactions. Using accurate MRCI potential energy surfaces (PESs), we obtain initial-state-resolved reaction probabilities, cross sections, and rate constants through the time-dependent, real wavepacket (WP) and flux methods, taking into account the proton-spin statistics for both electronic species. Comparing results on both PESs, we point out the role of the b (1)B(1) upper state on the initial-state-resolved dynamics and on the thermal kinetic rate. WP probabilities at J=0 and cross sections at E(col)=0.080 eV agree quite well with quantum-mechanical time-independent findings. Probabilities and WP snapshots show the different reaction mechanisms on the PESs, i.e., an ã (1)A(1) indirect perpendicular insertion and a b (1)B(1) direct sideways collision, associated with many and few sharp resonances, respectively. All cross sections are very large at low E(col), decrease at high energies, and that of the lowest reactant state presents some weak resonances. As the temperature increases from 100 to 400 K, the ã (1)A(1) rate constant increases slightly from 1.37x10(-10) to 1.43x10(-10) cm(3) s(-1), whereas the b (1)B(1) one decreases from 1.30x10(-10) to 0.98x10(-10) cm(3) s(-1). In this temperature range, the b (1)B(1) contribution to the total rate constant thus decreases from 49% to 41%. At 300 K, the WP and experimental rates are equal to (2.45+/-0.08)x10(-10) and (2.0+/-0.6)x10(-10) cm(3) s(-1), respectively.