The purpose of this paper is to give a characterization of
a locally inverse $*$-semigroup by introducing a new concept
of a {\it locally inductive $*$-groupoid}. Defining a
product $\otimes$ in a locally inductive $*$-groupoid $G$,
$G(\otimes )$ becomes a locally inverse $*$-semigroup.
Conversely, for a locally inverse $*$-semigroup $S$, we give
a partial product $\cdot$ in $S$, we show that
$S(\cdot, *, \leq )$ is a locally inductive $*$-groupoid and
that $S(\cdot, *, \leq )(\otimes ) = S$.