  Using the Double Chooz detector, designed to measure the neutrino mixing
angle $\theta_{13}$, the products of $\mu^-$ capture on $^{12}$C, $^{13}$C,
$^{14}$N and $^{16}$O have been measured. Over a period of 489.5 days,
$2.3\times10^6$ stopping cosmic $\mu^-$ have been collected, of which
$1.8\times10^5$ captured on carbon, nitrogen, or oxygen nuclei in the inner
detector scintillator or acrylic vessels. The resulting isotopes were tagged
using prompt neutron emission (when applicable), the subsequent beta decays,
and, in some cases, $\beta$-delayed neutrons. The most precise measurement of
the rate of $^{12}\mathrm C(\mu^-,\nu)^{12}\mathrm B$ to date is reported:
$6.57^{+0.11}_{-0.21}\times10^{3}\,\mathrm s^{-1}$, or
$(17.35^{+0.35}_{-0.59})\%$ of nuclear captures. By tagging excited states
emitting gammas, the ground state transition rate to $^{12}$B has been
determined to be $5.68^{+0.14}_{-0.23}\times10^3\,\mathrm s^{-1}$. The
heretofore unobserved reactions $^{12}\mathrm
C(\mu^-,\nu\alpha)^{8}\mathrm{Li}$, $^{13}\mathrm C(\mu^-,\nu\mathrm
n\alpha)^{8}\mathrm{Li}$, and $^{13}\mathrm C(\mu^-,\nu\mathrm n)^{12}\mathrm
B$ are measured. Further, a population of $\beta$n decays following stopping
muons is identified with $5.5\sigma$ significance. Statistics limit our ability
to identify these decays definitively. Assuming negligible production of
$^{8}$He, the reaction $^{13}\mathrm C(\mu^-,\nu\alpha)^{9}\mathrm{Li}$ is
found to be present at the $2.7\sigma$ level. Limits are set on a variety of
other processes.
