  We present Keck Cosmic Web Imager IFU observations around extended Ly$\alpha$
halos of 27 typical star-forming galaxies with redshifts $2.0 < z < 3.2$ drawn
from the MOSFIRE Deep Evolution Field survey. We examine the average Ly$\alpha$
surface-brightness profiles in bins of star-formation rate (SFR), stellar mass
($M_*$), age, stellar continuum reddening, SFR surface density ($\rm
\Sigma_{SFR}$), and $\rm \Sigma_{SFR}$ normalized by stellar mass ($\rm
\Sigma_{sSFR}$). The scale lengths of the halos correlate with stellar mass,
age, and stellar continuum reddening; and anti-correlate with star-formation
rate, $\rm \Sigma_{SFR}$, and $\rm \Sigma_{sSFR}$. These results are consistent
with a scenario in which the down-the-barrel fraction of Ly$\alpha$ emission is
modulated by the low-column-density channels in the ISM, and that the neutral
gas covering fraction is related to the physical properties of the galaxies.
Specifically, we find that this covering fraction increases with stellar mass,
age, and $E(B-V)$; and decreases with SFR, $\rm \Sigma_{SFR}$ and $\rm
\Sigma_{sSFR}$. We also find that the resonantly scattered Ly$\alpha$ emission
suffers greater attenuation than the (non-resonant) stellar continuum emission,
and that the difference in attenuation increases with stellar mass, age, and
stellar continuum reddening, and decreases with $\rm \Sigma_{sSFR}$. These
results imply that more reddened galaxies have more dust in their CGM.
