K2-18 b is a transiting mini-Neptune that orbits a nearby (38pc), cool M3 dwarf and is located inside its region of temperate irradiation. We report on the search for hydrogen escape from the atmosphere K2-18 b using Lyman-{alpha} transit spectroscopy with the Space Telescope Imaging Spectrograph (STIS) instrument installed on the Hubble Space Telescope (HST). We analyzed the time-series of fluxes of the stellar Lyman-{alpha} emission of K2-18 in both its blue- and redshifted wings. We found that the average blueshifted emission of K2-18 decreases by 67%+/-18% during the transit of the planet compared to the pre-transit emission, tentatively indicating the presence of H atoms escaping vigorously and being blown away by radiation pressure. This interpretation is not definitive because it relies on one partial transit. Based on the reconstructed Lyman-{alpha} emission of K2-18, we estimate an EUV irradiation in the range 10^1^-10^2^erg/s/cm^2^ and a total escape rate on the order of 10^8^g/s. The inferred escape rate suggests that the planet will lose only a small fraction (<1%) of its mass and retain its volatile-rich atmosphere during its lifetime. More observations are needed to rule out stellar variability effects, confirm the in-transit absorption, and better assess the atmospheric escape and high-energy environment of K2-18 b.