We present new H i spectral line imaging of the extremely metal-poor , star-forming dwarf irregular galaxy Leo P. Our H i images probe the global neutral gas properties and the local conditions of the interstellar medium ( ISM ) . The H i morphology is slightly elongated along the optical major-axis . We do not find obvious signatures of interaction or infalling gas at large spatial scales . The neutral gas disk shows obvious rotation , although the velocity dispersion is comparable to the rotation velocity . The rotation amplitude is estimated to be V _ { c } = 15 \pm 5 km s ^ { -1 } . Within the H i radius probed by these observations , the mass ratio of gas to stars is roughly 2:1 , while the ratio of the total mass to the baryonic mass is > \sim 15:1 . We use this information to place Leo P on the baryonic Tully-Fisher relation , testing the baryonic content of cosmic structures in a sparsely populated portion of parameter space that has hitherto been occupied primarily by dwarf spheroidal galaxies . We detect the signature of two temperature components in the neutral ISM of Leo P ; the cold and warm components have characteristic velocity widths of 4.2 \pm 0.9 km s ^ { -1 } and 10.1 \pm 1.2 km s ^ { -1 } , corresponding to kinetic temperatures of \sim 1100 K and \sim 6200 K , respectively . The cold H i component is unresolved at a physical resolution of 200 pc . The highest H i surface densities are observed in close physical proximity to the single H ii region . A comparison of the neutral gas properties of Leo P with other extremely metal-deficient ( XMD ) galaxies reveals that Leo P has the lowest neutral gas mass of any known XMD , and that the dynamical mass of Leo P is more than two orders of magnitude smaller than any known XMD with comparable metallicity .