The rotational spectra of the (20)Ne and (22)Ne isotopomers of the Ne-dimethyl sulfide (DMS) rare gas dimer have been measured by Fourier transform microwave spectroscopy. MP2/6-311++G(2d,2p) calculations, and the experimental spectroscopic data, suggest a structure of C(s) symmetry in which the Ne atom lies above the heavy atom plane of the DMS (in the sigma(v) plane which bisects the CSC angle). Experimental rotational constants are consistent with a S...Ne distance of 3.943(6) Angstroms and a (cm...S...Ne) angle of 63.2(6) degrees (where cm is the center of mass of DMS). A motion of the Ne atom from one side of the DMS to the other gives rise to inversion splittings of around 3 MHz in the c-type transitions. An ab initio potential energy surface calculation has allowed examination of several possible tunneling pathways, and suggests a barrier of between 20 and 40 cm(-1) for the inversion motion, depending on the tunneling pathway taken by the Ne. Dipole moment measurements are consistent with both the experimental and ab initio structures.