  We prove that a topological Clifford semigroup $S$ is metrizable if and only
if $S$ is an $M$-space and the set $E=\{e\in S:ee=e\}$ of idempotents of $S$ is
a metrizable $G_\delta$-set in $S$. The same metrization criterion holds also
for any countably compact Clifford topological semigroup $S$.
