Transverse-field muon spin-rotation measurements have been carried out on LaH_2.75 over the temperature range 15-300 K. The muon depolarisation rate sigma remains constant in the temperature range 15-160 K, indicating that in this region muons are immobile. The measured value of sigma is in good agreement with a rigid-lattice second-moment calculation based on the assumption that the muons occupy vacant octahedral interstitial sites. Motional averaging sets in about the same temperature (T>165 K) at which the NMR line narrowing due to proton diffusion occurs. The muon correlation time tau follows an Arrhenius-like behaviour up to T approximately= 240 K with an activation energy of 185 meV, which is very similar to that of the NMR value for the proton. The measured tau -value shows a sharp discontinuous drop by an order of magnitude at T approximately=241 K, a clear indication of a phase transition. The nature of this transition is discussed in relation to the heat capacity anomalies and lattice distortion observed at about the same temperature.