  We analyze the gas kinematics and star formation properties of the nearby
RSab galaxy NGC 4736 using interferometric and single-dish CO(1-0) data and
previously published Halpha and HI data. The CO morphology is dominated by a
central molecular bar and tightly wound spiral arms associated with a bright
ring of star formation. Strong HI emission is also found in the ring, but HI is
absent from the central regions. Comparison of the HI and Halpha distributions
suggests that HI in the ring is primarily dissociated H$_2$. Modeling of the CO
kinematics reveals gas motion in elliptical orbits around the central bar, and
we argue that the ring represents both the OLR of the bar and the ILR of a
larger oval distortion. The HI kinematics show evidence for axisymmetric inflow
towards the ring and are inconsistent with streaming in aligned elliptical
orbits, but the highly supersonic (~40 km/s) inflow velocities required,
corresponding to mass inflow rates of ~2 Msol/yr, suggest that more
sophisticated models (e.g., gas orbiting in precessed elliptical orbits) should
be considered. The radial CO and Halpha profiles are poorly correlated in the
vicinity of the nuclear bar, but show a better correlation (in rough agreement
with the Schmidt law) at the ring. Even along the ring, however, the azimuthal
correspondence between CO and Halpha is poor, suggesting that massive stars
form more efficiently at some (perhaps resonant) locations than at others.
These results indicate that the star formation rate per unit gas mass exhibits
strong spatial variations and is not solely a function of the available gas
supply. The localization of star formation to the ring is broadly consistent
with gravitational instability theory, although the instability parameter $Q
\sim 3$ on average in the ring, only falling below 1 in localized regions.
