  We investigate the role played by the fermionic determinant in the evaluation
of the CP-violating neutron electric dipole moment (EDM) adopting the Instanton
Liquid Model. Significant differences between quenched and unquenched
calculations are found. In the case of unquenched simulations the neutron EDM
decreases linearly with the quark mass and is expected to vanish in the chiral
limit. On the contrary, within the quenched approximation, the neutron EDM
increases as the quark mass decreases and is expected to diverge as (1/m)**Nf
in the chiral limit. We argue that such a qualitatively different behavior is a
parameter-free, semi-classical prediction and occurs because the neutron EDM is
sensitive to the topological structure of the vacuum. The present analysis
suggests that quenched and unquenched lattice QCD simulations of the neutron
EDM as well as of other observables governed by topology might show up
important differences in the quark mass dependence, for mq < Lambda(QCD).
