We present state-selected measurements of rotational cooling and excitation rates of CH^{+} molecular ions by inelastic electron collisions. The experiments are carried out at a cryogenic storage ring, making use of a monoenergetic electron beam at matched velocity in combination with state-sensitive laser dissociation of the CH^{+} ions for simultaneous monitoring of the rotational level populations. Employing storage times of up to 600 s, we create conditions where electron-induced cooling to the J=0 ground state dominates over radiative relaxation, allowing for the experimental determination of inelastic electron collision rates to benchmark state-of-the-art theoretical calculations. On a broader scale, our experiments pave the way to probe inelastic electron collisions for a variety of molecular ions relevant in various plasma environments.