Rotational spectra have been measured for six isotopomers of the dimethylamine dimer using a Fourier-transform microwave spectrometer. No tunneling splittings were observed for either the a- or c-type rotational transitions and the spectra could be fit to a rigid rotor Hamiltonian including centrifugal distortion terms. Possible dimer structures are discussed and compared to the experimentally determined moments of inertia, dipole moments, and nuclear quadrupole coupling constants. A cyclic structure with C-s symmetry was found to best reproduce the inertial data. The structure of the dimethylamine dimer is compared to the theoretical and experimental structures for the ammonia dimer.