We report on the search for a CPT and Lorentz invariance violating coupling of the 3He and 129Xe nuclear spins (each largely determined by a valence neutron) to background tensor fields which permeate the universe. Our experimental approach is to measure the free precession of nuclear spin polarized 3He and 129Xe atoms in a homogeneous magnetic guiding field of about 400 nT using LTC SQUIDs as low-noise magnetic flux detectors. As the laboratory reference frame rotates with respect to distant stars, we look for a sidereal modulation of the Larmor frequencies of the co-located spin samples. As a result we obtain an upper limit on the equatorial component of the background field interacting with the spin of the bound neutron bn< 6.7*10^-34 GeV (68% C.L.). Our result improves our previous limit (data measured in 2009) by a factor of 30 and the world's best limit by a factor of 5.