A tunable microwave-sideband CO2 laser is used with an electric-resonance optothermal spectrometer to investigate the infrared spectrum of CF3CH3 near 970 cm-1. A Fermi-coupled triad of states is observed, resulting from the interactions of 2nu6+nu11 and nu5+nu12 with the fundamental vibration, nu10, which is assumed to carry the oscillator strength in this region. The high resolution (approximately 3 MHz) of the spectrometer allows the observation of tunneling splittings associated with the nu6 torsional vibration. These splittings are used to identify the torsional character of the states observed. At the normal-mode level the nu10 and nu5 + nu12 states are found to be nearly degenerate and interacting by an anharmonic matrix element of approximately 3 cm-1. The lower-energy component of this diad exhibits torsional splittings of up to 400 MHz due to an anharmonic coupling of 0.70 cm-1 with the lower energy 2nu6+nu11 state which has an intrinsic tunneling splitting of approximately 800 MHz. A fourth state, 3nu6 + nu12, which has a still larger zeroth-order tunneling splitting, may also be affecting the torsional splittings of the observed states. The present investigation illustrates the utility of using resolved torsional splittings to unravel complex vibrational couplings in molecules.