  This paper is concerned with generalising the results for Lie $CT$-algebras
to Leibniz algebras. In some cases our results give a generalisation even for
the case of a Lie algebra. Results on $A$-algebras are used to show every
Leibniz $CT$-algebra over an algebraically closed field of characteristic
different from 2,3 is solvable or is isomorphic to $sl_2(F)$. A
characterisation is then given for solvable Leibniz $CT$-algebras. It is also
shown that the class of solvable Leibniz $CT$-algebras is factor closed.
