  The aim of this paper is to characterize the notion of internal category
(groupoid) in the category of Leibniz algebras and investigate the properties
of well-known notions such as covering groupoid and groupoid operations
(actions) in this category. Further, for a fixed internal groupoid $G$, we
prove that the category of covering groupoids of $G$ and the category of
internal groupoid actions of $G$ on Leibniz algebras are equivalent. Finally we
interpret the corresponding notion of covering groupoids in the category of
crossed modules of Leibniz algebras.
