EUV and soft X-ray-induced photofragmentation of the halothane (CF3CHBrCl) molecule has been investigated using time-of-flight mass spectrometry in the coincidence mode (PEPICO) covering the valence region and vicinity of the bromine 3d, chlorine 2p, and carbon 1s edges. Total and partial ion yields have been recorded as a function of photon energy. At lower photon energies, the heavier singly charged molecular fragments predominate in the mass spectra. On the other hand, there is a strong tendency to the atomization of the molecule at higher photon energies. Despite the different chemical environments experienced by the two carbon atoms, weak site-specific fragmentation is observed. In addition, ab initio quantum mechanical calculations at the MP2 level and a series of computations with multiconfigurational self-consistent field have been performed to describe the inner-shell states.