  Using a sample of galaxies at $z\approx 3$ with detected Lyman Continuum
(LyC) leakage in the SSA22 field, we attempt to verify a proposed indirect
method for identifying cases with high LyC escape fraction $f_\mathrm{esc}$
based on measurements of the H$\beta$ equivalent width (EW) and the $\beta$
slope of the UV continuum. To this end, we present Keck/MOSFIRE H$\beta$
emission line flux measurements of LyC galaxies (LCGs) at spectroscopic
redshifts $z_{\mathrm{spec}} \sim 3.3$, Lyman break galaxies (LBGs) at
photometric redshifts $z_{\mathrm{phot}} = 2.7$--$3.7$, and Ly$\alpha$ emitters
at $z_{\mathrm{phot}} = 3.1$. We also reconfirm the spectroscopic redshifts and
measure the H$\beta$ emission line fluxes from 2 LCGs and 6 LBGs. For the LCG
in our sample with the most extreme $f_\mathrm{esc}$, as revealed by the direct
detection of LyC photons, we find that the EW(H$\beta$)--$\beta$ method gives a
broadly consistent estimate for $f_\mathrm{esc}$, although the error bars
remain very large. We also discuss how a combination of $f_\mathrm{esc}$
measurements based on direct and indirect methods can shed light on the LyC
escape mechanism and the anisotropy of the leakage.
