We performed a search for neutron spin coupling to a Lorentz- and CPT-violating background field using a magnetometer with overlapping ensembles of K and 3He atoms. The co-magnetometer is mounted on a rotary platform for frequent reversal of its orientation. We measure sidereal oscillations in the signal to search for an anomalous spin coupling of an extrasolar origin. We limit the magnitude of equatorial components of the background field interacting with the neutron spin to be |bn| < 3.7 × 10-33 GeV at the 68% confidence level, improving on the previous limit by a factor of 30. This measurement represents the highest energy resolution of any spin anisotropy experiment.