We present Lyman continuum (LyC) radiation escape fraction ( 𝑓 esc ) measurements for 183 spectroscopically confirmed starforming 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 ] + H𝛽 equivalent widths (that fall in the observed 𝐾 band) by including nebular emission in the SED fitting. After removing foreground contaminants, we report the discovery of 11 new candidate LyC leakers, with absolute LyC escape fractions, 𝑓 esc in the range 0.07 − 0.52. Most galaxies in our sample (≈ 94%) do not show any LyC leakage, and we place 1𝜎 upper limits of 𝑓 esc < 0.07 through weighted averaging, where the Lyman-break selected galaxies have 𝑓 esc < 0.07 and 'blindly' discovered galaxies with no prior photometric selection have 𝑓 esc < 0.10. We additionally measure 𝑓 esc < 0.09 for extreme emission line galaxies in our sample with rest-frame [O ] + H𝛽 equivalent widths > 300 Å. For the candidate LyC leakers, we do not find a strong dependence of 𝑓 esc on their stellar masses and/or specific star-formation rates, and no correlation between 𝑓 esc and EW 0 ([O ] + H𝛽). We suggest that this lack of correlations may be explained by viewing angle and/or non-coincident timescales of starburst activity and periods of high 𝑓 esc . Alternatively, escaping radiation may predominantly occur in highly localised star-forming regions, thereby obscuring any global trends with galaxy properties. Both hypotheses have important consequences for models of reionisation.