We have searched for solid H2S absorption features in a sample of six objects, consisting of three high-mass protostars (Mon R2/IRS-2, Mon R2/IRS-3 and W3/IRS-5), and three late-type field stars lying behind the Taurus dark cloud (Elias 16, Elias 13 and Elias 3). No evidence is found for absorption by solid H2S in any of these six objects, and an absorbance value taken from the literature is used to place upper limits on the column densities of solid H2S in the lines-of-sight to these objects. We find that these upper limits are consistent with the proposal that H2S molecules are formed on grain surfaces and subsequently desorbed to re-supply the gas-phase. The spectra of the Taurus sources are essentially featureless, but several features are seen in the protostar spectra. However, these are shown to be due to molecular absorption features in the standard star used. Because a standard of similar spectral type was used in a previous study which identified H2S absorption in W33A, it is argued that this identification is incorrect, or at least severely overestimates the amount of H2S present.