Two triaxial states of the proton-decaying nucleus 147Tm were studied via a comparison of experimental data to results obtained through nonadiabatic quasiparticle calculations. The experimental data were collected in a recoil-decay tagging study using the vacuum-mode recoil separator MARA coupled with the JUROGAM3 γ-ray spectrometer. The previously proposed level scheme above the triaxial 11/2− (πh11/2) ground state was confirmed, and the level structure was expanded to cover the states above the weakly populated proton-emitting 5/2+ (πd5/2) isomeric state. It was found that the isomeric state is also triaxial, and possibly more deformed than the ground state.