The cause of HI velocity dispersions in the interstellar medium (ISM) of galaxies is often attributed to star formation, but recent evidence has shown these two quantities are not connected in regions of low star formation. This lack of connection is most apparent in dwarf galaxies and the outer disks of spiral galaxies. However, unique data sets have recently been collected that can help address this discrepancy. The ACS Nearby Survey Treasury Project (ANGST) has measured time-resolved star formation histories (SFHs) in ~70 nearby galaxies. The followup Very Large Array-ANGST survey (VLA-ANGST) provides complementary HI observations of a subset of ANGST galaxies. In this thesis, I explore the connection between star formation and HI kinematics in a number of nearby dwarf galaxies. I first present the Very Large Array-ACS Nearby Galaxy Survey Treasury Project (ANGST). VLA-ANGST was designed to provide high spatial and velocity resolution observations of the HI component of the interstellar medium (ISM) in ANGST galaxies. I describe the data calibration and imaging procedures, and then present the publicly-available data products. The observations from this survey and from The HI Nearby Galaxy Survey (THINGS) comprise the majority of data in my thesis. Using VLA-ANGST and THINGS data, I present a method to measure the average HI kinematics in a number of nearby dwarf galaxies by co-adding individual line-of-sight profiles. These "superprofiles" are composed of a central narrow peak (6-10 km/s) with higher velocity wings to either side. When scaled to the same half-width half-maximum, the shapes of the superprofiles are very similar. I interpret the central peak as representative of the average turbulent motion; the wings are then due to HI moving faster than expected compared to the average kinematics. I then compare the superprofile parameters to physical properties such as mass surface density and star formation intensity. The average velocity dispersion correlate most strongly with HI surface density, and do not show correlations with star formation intensity unless higher mass galaxies were included. The properties of the wings are more connected with star formation. By applying energy arguments, I determine that star formation can provide enough energy to drive the HI kinematics over 10 Myr timescales, while a gravitational instability cannot. I then extend this analysis to spatially-resolved scales in these galaxies, and generated superprofiles in regions determined by radius or by star formation intensity. These superprofiles provide a more direct comparison between HI kinematics and local ISM properties compared to the analysis on global scales. The spatially-resolved superprofiles indicate that star formation does not uniquely determine the HI velocity dispersion, but it does appear to provide a lower floor below which velocity dispersions cannot fall. I also find that the coupling efficiency between star formation and HI kinematics decreases with increasing star formation surface density, which may indicate that star formation energy couples more consistently to other phases of the ISM. I finally explore the timescale over which HI responds to star formation using a combination of VLA-ANGST, THINGS, and ANGST data. Using time-resolved SFHs from ANGST, I measure the average star formation rate as a function of time and compared it to present-day HI kinematics. I find that the HI kinematics are most strongly correlated with star formation that occurred 30-40 Myr ago, which supports the idea that supernova explosions are one driver of HI kinematics even in low star formation systems.