Climate change is increasing the frequency and magnitude of extreme rainfall events, exacerbating flood risk in urban areas. Floods represent the main cause of dam overtopping. Therefore, a warmer climate can affect hydrological dam safety, leading to an increase of overtopping probability in the future. In this context, new methodologies are required to assess the impact of climate change on hydrological dam safety. This study provides a stochastic methodology that considers the impact of climate change on floods (inflow hydrographs in the reservoir) and on the probability of a given water level in the reservoir in the future. Moreover, an uncertainty chain analysis is done to consider all the sources of errors in the methodology. A fully distributed hydrological model, the Real-time Interactive Basin Simulator (RIBS) model, is used to assess the impact of climate on flood quantiles at a sub-daily scale. The continuous HBV hydrological model is combined with a reservoir operation model to assess the future initial reservoir water level frequency at a daily scale. An ensemble of 12 climate models provides the climate projections for two emission scenarios (RCP 4.5 and RCP 8.5) and three time windows (2011-2040, 2041-2070, 2071-2100). The results show an increase in the future of maxima reservoir water levels associated with the most extreme events, especially in the 2071-2100 time window and RCP 8.5. Overtopping probability also increases in this latter scenario, while no changes are expected for the RCP 4.5.