The microwave spectra of CF3COSH and one deuterated species, CF3COSD, have been investigated by Stark spectroscopy in the 40-80 GHz spectral range at -78 degrees C and by quantum chemical calculations using the HF, MP2, and B3LYP procedures with the aug-cc-pVTZ basis set. The microwave spectrum of one conformer was assigned. The conformations of the COSH and CF3 groups determine the overall conformation of this rotamer. It was not possible experimentally to find precise values for the associated dihedral angles, but it appears that the COSH group is distorted somewhat from an exact synperiplanar arrangement, while the CF3 group is rotated several degrees from a position where one of the C-F bonds eclipses the C-S bond. This rotamer tunnels through a transition state that has an exact C-s symmetry, where one C-F bond eclipses the C-S bond and the COSH group is synperiplanar. Relative intensity measurements yielded 28(15) cm(-1) for the tunneling frequency. Two additional vibrationally excited states were assigned and their frequencies determined to be 94(30) and 184(40) cm(-1), respectively. The theoretical calculations predict conflicting conformational properties for the identified rotamer. The B3LYP calculations find an exact synperiplanar arrangement for the COSH group, whereas the MP2 and HF calculations predict that this group is distorted slightly form this conformation. One of the C-F bonds is found to eclipse the C-S bond in the B3LYP calculations, while the MP2 calculations predict a slight deviation and the HF calculations a large deviation from the eclipsed position, as the corresponding F-C-C-S dihedral angle is calculated to be 0.9 degrees (MP2) and 27.6 degrees (HF). All three methods of calculations predict that a second rotamer coexists with the identified form but is several kJ/mol less stable. The spectrum of this form, which has overall C-s symmetry and is predicted to have an antiperiplanar conformation for the COSH group with one of the C-F bonds eclipsing the CO bond, was not identified.