Selective screenability in topological groups

We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations of Sc(Onbd,O) and Smirnov-Sc(Onbd,O) in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We prove theorems stating conditions under which Sc(Onbd,O) is preserved by products. Among metrizable groups we characterize the countable dimensional ones by a natural game.