  We searched for a sidereal modulation in the rate of neutrinos produced by
the NuMI beam and observed by the MINOS far detector. The detection of such
harmonic signals could be a signature of neutrino-antineutrino mixing due to
Lorentz and CPT violation as described by the Standard Model Extension
framework. We found no evidence for these sidereal signals and we placed limits
on the coefficients in this theory describing the effect. This is the first
report of limits on these neutrino-antineutrino mixing coefficients.
