  We consider electron-atom scattering in a circularly polarized laser field at
sufficiently high electron energies, permitting to describe the scattering
process by the first order Born approximation. Assuming the radiation field has
sufficiently moderate intensities, the laser-dressing of the hydrogen target
atom in its ground state will be treated in second order perturbation theory.
Within this approximation scheme, it is shown that the nonlinear differential
cross sections of free-free transitions do neither depend on the {\it dynamical
phase} $\phi$ of the radiative process nor on the {\it helicity} of the
circularly polarized laser light. Relations to the corresponding results for
linear laser polarization are established.
