  We present an analysis of the relationship between molecular gas and current
star formation rate surface density at sub-kpc and kpc scales in a sample of 14
nearby star-forming galaxies. Measuring the relationship in the bright, high
molecular gas surface density ($\Shtwo\gtrsim$20 \msunpc) regions of the disks
to minimize the contribution from diffuse extended emission, we find an
approximately linear relation between molecular gas and star formation rate
surface density, $\nmol\sim0.96\pm0.16$, with a molecular gas depletion time
$\tdep\sim2.30\pm1.32$ Gyr. We show that, in the molecular regions of our
galaxies there are no clear correlations between \tdep\ and the free-fall and
effective Jeans dynamical times throughout the sample. We do not find strong
trends in the power-law index of the spatially resolved molecular gas star
formation law or the molecular gas depletion time across the range of galactic
stellar masses sampled (\mstar $\sim$$10^{9.7}-10^{11.5}$ \msun). There is a
trend, however, in global measurements that is particularly marked for low mass
galaxies. We suggest this trend is probably due to the low surface brightness
CO, and it is likely associated with changes in CO-to-H2 conversion factor.
