Dissociation of different compounds?
$\ce{H2S}$ has a mostly covalent character. You can decide for it by the crude way textbooks give: Calculate the difference in electronegativity to decide whether it's a non-polar covalent compound, a polar one or has ionic characters.
For the dissociation part (which is usually endothermic overall) it'll need more &quot;ionic character&quot;. And it does dissociate in water, resulting in a weak acid named  sulfhydric acid. (The spelling varies with citable sources) Your textbook likes to think about it as not dissociable, only because it's a weak acid.
Addendum:
The &quot;ionic character&quot; plays its role of a rule a good one as explaining acid 'strength'. However, it acts almost flawlessly in the same period, but has exceptions when it gets to groups. As Dave mentions, $\ce{HF}$ is weaker than for instance, $\ce{HCl}$ and that's because the atomic radius changes more dramatically than electronegativity difference. (See here ) But, in the $\ce{H2S}$ molecule, this exception hasn't occurred. Dave pointed out a good example of when the rule isn't working that well, but as I said, we can ignore the other factors in this very case.