The connection between the escape fraction of ionizing radiation (f esc ) and the properties of galaxies, such as stellar mass (M * ), age, star-formation rate (SFR), and dust content, are key inputs for reionization models, but many of these relationships remain untested at high redshift. We present an analysis of a sample of 96 z ∼ 3 galaxies from the Keck Lyman Continuum Spectroscopic Survey (KLCS). These galaxies have both sensitive Keck/LRIS spectroscopic measurements of the Lyman continuum (LyC) region, and multi-band photometry that places constraints on stellar population parameters. We construct composite spectra from subsamples binned as a function of galaxy property and quantify the ionizing-photon escape for each composite. We find a significant anti-correlation between f esc and M * , consistent with predictions from cosmological zoom-in simulations. We also find significant anti-correlation between f esc and E(B-V), encoding the underlying physics of LyC escape in our sample. We also find no significant correlation between f esc and either stellar age or specific SFR (=SFR/M * ), challenging interpretations that synchronize recent star formation and favorable conditions for ionizing escape. The galaxy properties now shown to correlate with f esc in the KLCS are Lyα equivalent width, UV Luminosity, M * , SFR, and E(B-V), but not age or sSFR. To date, this is the most comprehensive analysis of galaxy properties and LyC escape at high redshift, and will be used to guide future models and observations of the reionization epoch.