Sub-Doppler infrared spectra of five normal-mode vibrations of propene between 900-1100 cm-1 reveal strongly perturbed torsional tunneling splittings due to nonresonant anharmonic couplings to vibrational states in which the torsional mode is excited. The present results suggest that perturbed tunneling splittings will be a general feature for vibrationally excited states. Consequently, care should be taken when using tunneling splittings to obtain the vibrational dependence of a tunneling barrier. Instead, tunneling splittings in excited states can be used as a probe of long-range vibrational-torsional state mixing in molecules.