  We use a sample of 13,511 nearby galaxies from the ALFALFA and SDSS
spectroscopic surveys to study the relation between the spatial distribution of
H I 21 cm emission and star formation rate (SFR). We introduce a new
non-parametric quantity $K$, measured from the curve-of-growth of the line, to
describe the shape of the integrated H I profile. The value of $K$ increases
from double-horned to single-peaked profiles, depending on projection effects
and the spatial and velocity distribution of the gas. Using carefully chosen
samples to control for the competing factors that influence the integrated line
profile, we argue that useful inferences can be made on the spatial
distribution of the gas. We find that galaxies with a high value of $K$ tend to
have more centrally concentrated H I distribution within the optical disk of
the galaxy at fixed conditions, and that larger values of $K$ are associated
with higher levels of total and central SFR. The results suggest that the
global concentration of H I plays an important role in facilitating the
conversion of neutral atomic hydrogen to molecular hydrogen gas, which, in
turn, affects the star formation activity throughout the optical disk. Our
sample is biased against quiescent galaxies, and thus the conclusions may not
hold for galaxies with low SFR or low H I content.
