We present Lyman continuum (LyC) radiation escape fraction (f(esc)) measurements for 183 spectroscopically confirmed star-forming galaxies in the redshift range 3.11 < z < 3.53 in the Chandra Deep Field South. We use ground-based imaging to measure f(esc), and use ground- and space-based photometry to derive galaxy physical properties using spectral energy distribution (SED) fitting. We additionally derive [O iii] + H beta equivalent widths (that fall in the observed K band) by including nebular emission in SED fitting. After removing foreground contaminants, we report the discovery of 11 new candidate LyC leakers at greater than or similar to 2 sigma level, with f(esc) in the range 0.14-0.85. From non-detections, we place 1 sigma upper limits of f(esc) <0.12, where the Lyman-break selected galaxies have f(esc) f(esc) f(esc) iii] + H beta equivalent widths >300 angstrom. For candidate LyC leakers, we find a weak negative correlation between f(esc) and galaxy stellar masses, no correlation between f(esc) and specific star-formation rates (sSFRs) and a positive correlation between f(esc) and EW0([O iii] + H beta). The weak/no correlations between stellar mass and sSFRs may be explained by misaligned viewing angles and/or non-coincident time-scales of starburst activity and periods of high f(esc). Alternatively, escaping radiation may predominantly occur in highly localized star-forming regions, or f(esc) measurements may be impacted by stochasticity of the intervening neutral medium, obscuring any global trends with galaxy properties. These hypotheses have important consequences for models of reionization.