Turbulence has the potential for creating gas density enhancements that initiate cloud and star formation (SF), and it can be generated locally by SF. To study the connection between turbulence and SF, we looked for relationships between SF traced by FUV images, and gas turbulence traced by kinetic energy density (KED) and velocity dispersion ($v_{disp}$) in the LITTLE THINGS sample of nearby dIrr galaxies. We performed 2D cross-correlations between FUV and KED images, measured cross-correlations in annuli to produce correlation coefficients as a function of radius, and determined the cumulative distribution function of the cross correlation value. We also plotted on a pixel-by-pixel basis the locally excess KED, $v_{disp}$, and HI mass surface density, $Sigma_{rm HI}$, as determined from the respective values with the radial profiles subtracted, versus the excess SF rate density $Sigma_{rm SFR}$, for all regions with positive excess $Sigma_{rm SFR}$. We found that $Sigma_{rm SFR}$ and KED are poorly correlated. The excess KED associated with SF implies a $sim0.5$% efficiency for supernova energy to pump local HI turbulence on the scale of resolution here, which is a factor of $sim2$ too small for all of the turbulence on a galactic scale. The excess $v_{disp}$ in SF regions is also small, only $sim0.37$ km s$^{-1}$. The local excess in $Sigma_{rm HI}$ corresponding to an excess in $Sigma_{rm SFR}$ is consistent with an HI consumption time of $sim1.6$ Gyr in the inner parts of the galaxies. The similarity between this timescale and the consumption time for CO implies that CO-dark molecular gas has comparable mass to HI in the inner disks.
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