We measured the thresholds for photodetachment from the first and second excited rotational levels of CH− to the lowest vibrational, rotational, and fine-structure level of CH to be E1 = 1.213 ± 0.002 eV and E2 = 1.206 ± 0.002 eV, respectively. Based on these measurements and the rigid rotor approximation, we arrive at an electron affinity of EA = E1 + 1/2 (E1 − E2 ) = 1.217 ± 0.002 eV. This value deviates from earlier experimental results but agrees with the calculation by Feller [J. Chem. Phys. 144, 014105 (2016)]. In the present experiment, we stored ensembles of initially hot CH− in the cryogenic ion-beam storage ring Double ElectroStatic Ion-Ring ExpEriment (DESIREE) for tens of seconds such that the vast majority of the ions were in the few lowest excited rotational levels of the electronic and vibrational ground state.We identified the initial states for photodetachment channels with threshold energies E1 and E2 by comparing the time dependences of measured photodetachment signals with radiative rotational-cooling rates calculated using the literature values of the dipole moment of CH−. The conditions of a few occupied rotational levels are superior to those of previous studies of this system and an important step toward future studies with an all-rotational-ground-state ion beam.