Muon spin rotation (mu SR) experiments on single-crystal samples of ScHx, with x = 0, 0.05, 0.10 and 0.25, were performed in order to investigate the muon location and possible systematic variations in muon dynamics in these systems. The angular and magnetic field dependence of the mu SR relaxation rates shows that at temperatures below 50 K the muon is localized at the interstitial tetrahedral (T) sites. The results for pure Sc, covering a wide range of high and low fields, are coherent with the picture that the muon performs fast tunnelling between two adjacent T sites, separated by 2z = 0.18c, above and below the a-b plane. This value for the muon position along the c axis is remarkably near the 2z = 0.194c found for D in Sc by neutron diffraction. The anisotropy of the relaxation rate at low magnetic fields varies sensitively with the H concentration, indicating a change in the ratio of the radial, muon-induced and the partly inherent, uniaxial electric field gradients at the position of the Sc nuclei.