We present accurate ab initio calculations on several properties of a gas-phase system of interest in the interstellar medium (ISM), where the title molecular anion has been often surmised but not yet confirmed by observations. The CH-3Σ+ constitutes the smallest term in the series of longer anionic polyynes which have been observed in the ISM (e.g., C4H- and several others). Hence, its dynamical behavior in collision with He atoms, one of the most abundant atoms in that environment, can provide quantitative indicators on the changes which can occur in the rotational state population of the title anion when driven by this collision dynamics. We therefore report an accurate evaluation of the full potential energy surface (PES) which acts between the molecular anion in its ground vibrational state and the He atom. The relevant inelastic scattering cross sections and the corresponding inelastic rate coefficients are then computed within a quantum treatment of the collisions. We find that the fairly small values of the final inelastic rate coefficients indicate state-changing processes by collisions to be inefficient paths for modifying the rotational state populations of this anion and therefore to aid its possible observation from direct radiative emission in the microwave region.