The scattering of neutrons by a polycrystalline sample of tetramethylammonium manganese chloride has been measured for 0-500 cm-1 energy transfers, both below and above the phase transition at 128 K. In the 0-50 cm-1 region, which reflects the rotational motion of the polyatomic cations, the scattered spectrum exhibits an inelastic peak at low temperature, but only a shoulder extending from the quasi-elastic peak in the high temperature phase. These spectra are semi-quantitatively interpreted by a model which assumes that the tetramethylammonium ions experience a three-well crystalline field and random torque-impulses for simulating the contact with the thermal bath. The fit of this model to the experimental data shows that the potential barrier is sufficiently high in the low temperature phase for the cations to perform a librational motion of relatively long duration in a given well. By contrast, in the high temperature phase, the motion is rather that of a slightly hindered rotator.