  We investigate the conformal transformation of vierbein-Einstein-Palatini
(VEP) action in terms of tetrads $e^I_\mu$ and spin connection $A^{IJ}_\mu$.
The transformation of the spin connection is indeterminate off-shell unless
equations of motion are satisfied. We construct the conformally invariant
scalar field in the torsion-free VEP formalism. In presence of fermionic
matter, torsion does not vanish, and shows up in the dynamics of conformal
scalar, affecting the invariance. It is not possible to maintain conformal
invariance of the scalar field equation when fermions are present.
