Rate coefficients of the complex-forming C + NH→H + CN reaction have been calculated at temperatures ranging from 5 K to 800 K using quasi-classical trajectories on a potential energy surface which accurately describes the attractive long-range interaction, along with results using two capture models. In contrast with the constant value recommended in astrochemical databases, a steep decrease of the rates has been found up to 150 K, and then they tends to be nearly constant. Such behavior is analyzed in terms of the rovibrational state-selected rate coefficients and cross sections singling out the role played by the rotational excitation of the initial diatom. The effect of the electronic degeneracy is also discussed.