The dielectric response of liquids in the terahertz (THz) and sub-THz frequency range arises from low-energy collective molecular motions, which are often strongly influenced by intermolecular interactions. To shed light on the microscopic origin of the THz dielectric response of the simplest alcohol, methanol, we resonantly excite this liquid with an intense THz electric-field pulse and monitor the relaxation of the induced optical birefringence. We find a unipolar THz-Kerr-effect signal which, in contrast to aprotic polar liquids, shows a weak coupling between the THz electric field and the permanent molecular dipole moment of the liquid. We assign this weak coupling to the restricted translational rather than rotational nature of the excited mode. Our approach opens a new avenue to the assignment of the dielectric spectrum of liquids to a microscopic origin.