  There is accumulating evidence for a difference between neutrino and
antineutrino oscillations at the $\sim 1$ eV$^2$ scale. The MiniBooNE
experiment observes an unexplained excess of electron-like events at low
energies in neutrino mode, which may be due, for example, to either a neutral
current radiative interaction, sterile neutrino decay, or to neutrino
oscillations involving sterile neutrinos and which may be related to the LSND
signal. No excess of electron-like events ($-0.5 \pm 7.8 \pm 8.7$), however, is
observed so far at low energies in antineutrino mode. Furthermore, global 3+1
and 3+2 sterile neutrino fits to the world neutrino and antineutrino data
suggest a difference between neutrinos and antineutrinos with significant
($\sin^22\theta_{\mu \mu} \sim 35%$) $\bar \nu_\mu$ disappearance. In order to
test whether the low-energy excess is due to neutrino oscillations and whether
there is a difference between $\nu_\mu$ and $\bar \nu_\mu$ disappearance, we
propose building a second MiniBooNE detector at (or moving the existing
MiniBooNE detector to) a distance of $\sim 200$ m from the Booster Neutrino
Beam (BNB) production target. With identical detectors at different distances,
most of the systematic errors will cancel when taking a ratio of events in the
two detectors, as the neutrino flux varies as $1/r^2$ to a calculable
approximation. This will allow sensitive tests of oscillations for both $\nu_e$
and $\bar \nu_e$ appearance and $\nu_\mu$ and $\bar \nu_\mu$ disappearance.
Furthermore, a comparison between oscillations in neutrino mode and
antineutrino mode will allow a sensitive search for CP and CPT violation in the
lepton sector at short baseline ($\Delta m^2 > 0.1$ eV$^2$).
