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 $S(\cdot, *, \leq )(\otimes ) = S$.