We have developed the polyatomic extension of a recently established (M. Gustafsson, J. Chem. Phys, 138, 074308 ( 2013)) classical theory of radiative association in the absence of electronic transitions. The cross section of the process is calculated by a quasiclassical trajectory method combined with the classical Larmor formula which can provide the radiated power in collisions. We have also proposed a double-layered Monte Carlo scheme for efficient computation of ro-vibrationally quantum state resolved cross sections for radiative association. Besides the method development, we also calculated and fitted the global potential energy and dipole surface for the H + CN collisions to test our polyatomic semiclassical method.