We have studied the relationship between the star formation rate (SFR), surface density, and gas surface density in the spiral galaxy M51a (NGC 5194), using multiwavelength data obtained as part of the Spitzer Infrared Nearby Galaxies Survey (SINGS). We introduce a new SFR index based on a linear combination of Hα emission-line and 24 μm continuum luminosities, which provides reliable extinction-corrected ionizing fluxes and SFR densities over a wide range of dust attenuations. The combination of these extinction-corrected SFR densities with aperture synthesis H I and CO maps has allowed us to probe the form of the spatially resolved star formation law on scales of 0.5-2 kpc. We find that the resolved SFR versus gas surface density relation is well represented by a Schmidt power law, which is similar in form and dispersion to the disk-averaged Schmidt law. We observe a comparably strong correlation of the SFR surface density with the molecular gas surface density, but no significant correlation with the surface density of atomic gas. The best-fitting slope of the Schmidt law varies from N = 1.37 to 1.56, with zero point and slope that change systematically with the spatial sampling scale. We tentatively attribute these variations to the effects of areal sampling and averaging of a nonlinear intrinsic star formation law. Our data can also be fitted by an alternative parameterization of the SFR surface density in terms of the ratio of gas surface density to local dynamical time, but with a considerable dispersion.