Some extensions of standard particle physics postulate that dark matter may be partially composed of weakly-interacting sterile neutrino particles that have so far eluded detection . We use a short ( \sim 5 ks ) archival X-ray observation of Segue 1 obtained with the X-Ray Telescope ( XRT ) on board the Swift satellite to exclude the presence of sterile neutrinos in the 1.6–14 keV mass range down to a flux limit of 6 \times 10 ^ { -12 } ergs cm ^ { -2 } s ^ { -1 } within 67 pc of its center . With an estimated mass-to-light ratio of \sim 3400 M _ { \odot } /L _ { \odot } , Segue 1 is the darkest ultra-faint dwarf galaxy currently measured . Spectral analysis of the Swift XRT data fails to find any non-instrumental spectral feature possibly connected with the radiative decay of a dark matter particle . Accordingly , we establish upper bounds on the sterile neutrino parameter space based on the non-detection of emission lines in the spectrum . The present work provides the most sensitive X-ray search for sterile neutrinos in a region with the highest dark matter density yet measured .