Deuteron nuclear magnetic resonance was employed to study primarily the glassy phase of the fragile glass-former propylene carbonate, selectively deuterated at the methyl group. The analysis of temperature dependent line shapes allowed us to map out the energy barrier distribution below the glass transition temperature. The results were compared to measurements of spin-relaxation times. We determined the relative width of the barrier distribution and the extent of the decoupling between the methyl group rotation time and the structural relaxation time near the glass transition. These findings are discussed in the context of what has been reported for secondary relaxation processes in other glass-formers. Stimulated echo experiments on propylene carbonate demonstrate that, while in the supercooled liquid small angle reorientations dominate, in the glass the methyl group performs 120° (or 60°) jumps.