  We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It
is shown that the Noether currents for both Weyl symmetry and global scale
symmetry, identically vanish as in the conformally invariant scalar-tensor
gravity. We clearly explain why in the class of conformally invariant
gravitational theories, the Noether currents vanish by starting with the
conformally invariant scalar-tensor gravity. Moreover, we comment on both
classical and quantum-mechanical equivalences among Einstein's general
relativity, the conformally invariant scalar-tensor gravity and the
Weyl-transverse (WTDiff) gravity. Finally, we discuss the Weyl current in the
conformally invariant scalar action and see that it is also vanishing.
