  Recent work suggests that strong emission line, star-forming galaxies may be
significant Lyman Continuum leakers. We combine archival HST broadband
ultraviolet and optical imaging (F275W and F606W, respectively) with emission
line catalogs derived from WFC3 IR G141 grism spectroscopy to search for
escaping Lyman Continuum (LyC) emission from homogeneously selected
$z\simeq$2.5 SFGs. We detect no escaping Lyman Continuum from SFGs selected on
[OII] nebular emission (N=208) and, within a narrow redshift range, on
[OIII]/[OII]. We measure 1$\sigma$ upper limits to the LyC escape fraction
relative to the non-ionizing UV continuum from [OII] emitters, $f_{esc}<$5.6%,
and strong [OIII]/[OII]$>$5 ELGs, $f_{esc}<$14.0%. Our observations are not
deep enough to detect $f_{esc}\lesssim$10% typical of the low redshift Lyman
continuum emitters. However, we find that this population represents a small
fraction of the star-forming galaxy population at $z\simeq$2. Thus, unless the
number of extreme emission line galaxies grows substantially to z$>$6, such
galaxies may be insufficient for reionization. Deeper survey data in the
rest-frame ionizing UV will be necessary to determine whether strong line
ratios could be useful for pre-selecting LyC leakers at high redshift.
