  In this article we investigate the interplay between stem covers, the Schur
multiplier of Leibniz crossed modules and the non-abelian exterior product of
Leibniz algebras. In concrete, we obtain a six-term exact sequence associated
to a central extension of Leibniz crossed modules, which is useful to
characterize stem covers. We show the existence of stem covers and determine
the structure of all stem covers of Leibniz crossed modules. Also, we give the
connection between the stem cover of a Lie crossed module in the categories of
Lie and Leibniz crossed modules respectively.
