The role of polarization has been systematically studied for the methylchloromethane family ((CH3)(4-n)CCln) of organic liquids. Special attention has been paid to dynamical properties (translational diffusion and rotational relaxation) for which good agreement with experiment is obtained, although structural and electrostatic effects have been addressed as well. Molecular dynamics simulations have been performed, with and without the inclusion of polarization, over a substantial range of temperatures. Polarizability has been handled with the chemical potential equalization (fluctuating charge) method, with a transferable set of parameters having been developed for the methyl group. As a general rule, the inclusion of polarization does not affect structure and slightly slows down the dynamics at all temperatures. The overall muted influence of polarization contrasts with the substantial induced dipole moments obtained, exceeding what had been found in other organic (albeit hydrogen-bonding) liquids.