We investigated dimethyl-s-tetrazine (-h(6) and -d(6)) in a n-heptane (-h(16) and -d(16)) lattice with hole burning techniques. Stark experiments definitely show that the two methyl groups in dimethyl-s-tetrazine (DMST) are inequivalent. Hence, the respective rotational tunneling dynamics can be different. This is clearly seen in the behavior of DMST-d(6) in both lattices n-heptane-h(16) and -d(16) : Hole burning produces three pairs of sideholes symmetrically shifted from the laser frequency. The tunneling dynamics of the central hole as well as of the sideholes is governed by two relaxation times which differ by about one order of magnitude. Due to the narrow temperature range accessible, and unambiguous assignment of the microscopic tunneling relaxation process is not possible. On the other hand, DMST-h(6) relaxes via a Raman process above 3 K and via a direct process below. In the Raman-active regime the tunneling rates for both host lattices fall on top of each other in agreement with theory. There are, however, features in the tunneling dynamics which are not yet understood. For instance, in the temperature regime where the direct process prevails, host deuteration speeds up the tunneling relaxation by an order of magnitude. In addition, th sidehole pattern of DMST-h(6) is quite different from DMST-d(6) : Only one pair is observed.