  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 the 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.
