We present kinematic analyses of the 12 galaxies in the "Survey of H I in Extremely Low-mass Dwarfs" (SHIELD). We use multi-configuration interferometric observations of the H I 21 cm emission line from the Karl G. Jansky Very Large Array (VLA) 22 to produce image cubes at a variety of spatial and spectral resolutions. Both two-and three-dimensional fitting techniques are employed in an attempt to derive inclination-corrected rotation curves for each galaxy. In most cases, the comparable magnitudes of velocity dispersion and projected rotation result in degeneracies that prohibit unambiguous circular velocity solutions. We thus make spatially resolved position-velocity cuts, corrected for inclination using the stellar components, to estimate the circular rotation velocities. We find v circ  30 km s −1 for the entire survey population. Baryonic masses are calculated using singledish H I fluxes from Arecibo and stellar masses derived from HST and Spitzer imaging. Comparison is made with total dynamical masses estimated from the position-velocity analysis. The SHIELD galaxies are then placed on the baryonic Tully-Fisher relation. There exists an empirical threshold rotational velocity, Vrot < 15 km s −1 , below which current observations cannot differentiate coherent rotation from pressure support. The SHIELD galaxies are representative of an important population of galaxies whose properties cannot be described by current models of rotationally dominated galaxy dynamics.

We analyze the relationships between atomic, neutral hydrogen (H I) and star formation (SF) in the 12 low-mass SHIELD galaxies. We compare high spectral (∼0.82 km s −1 ch −1 ) and spatial resolution (physical resolutions of 170 pc -700 pc) H I imaging from the VLA with Hα and far-ultraviolet imaging. We quantify the degree of co-spatiality between star forming regions and regions of high H I column densities. We calculate the global star formation efficiencies (SFE, Σ SFR / Σ H I ), and examine the relationships among the SFE and H I mass, H I column density, and star formation rate (SFR). The systems are consuming their cold neutral gas on timescales of order a few Gyr. While we derive an index for the Kennicutt-Schmidt relation of N ≈ 0.68±0.04 for the SHIELD sample as a whole, the values of N vary considerably from system to system. By supplementing SHIELD results with those from other surveys, we find that HI mass and UV-based SFR are strongly correlated over five orders of magnitude. Identification of patterns within the SHIELD sample allows us to bin the galaxies into three general categories: 1) mainly co-spatial H I and SF regions, found in systems with highest peak H I column densities and highest total H I masses; 2) moderately correlated H I and SF regions, found in systems with moderate H I column densities; and 3) obvious offsets between H I and SF peaks, found in systems with the lowest total H I masses. SF in these galaxies is dominated by stochasticity and random fluctuations in their ISM.