  Molecular species, most frequently H_2, are present in a small, but growing,
number of gamma-ray burst (GRB) afterglow spectra at redshifts z~2-3, detected
through their rest-frame UV absorption lines. In rare cases, lines of
vibrationally excited states of H_2 can be detected in the same spectra. The
connection between afterglow line-of-sight absorption properties of molecular
(and atomic) gas, and the observed behaviour in emission of similar sources at
low redshift, is an important test of the suitability of GRB afterglows as
general probes of conditions in star formation regions at high redshift.
Recently, emission lines of carbon monoxide have been detected in a small
sample of GRB host galaxies, at sub-mm wavelengths, but no searches for H_2 in
emission have been reported yet. In this paper we perform an exploratory search
for rest-frame K band rotation-vibrational transitions of H_2 in emission,
observable only in the lowest redshift GRB hosts (z<0.22). Searching the data
of four host galaxies, we detect a single significant rotation-vibrational H_2
line candidate, in the host of GRB 031203. Re-analysis of Spitzer mid-infrared
spectra of the same GRB host gives a single low significance rotational line
candidate. The (limits on) line flux ratios are consistent with those of blue
compact dwarf galaxies in the literature. New instrumentation, in particular on
the JWST and the ELT, can facilitate a major increase in our understanding of
the H_2 properties of nearby GRB hosts, and the relation to H_2 absorption in
GRBs at higher redshift.
