  In this paper, we study McKean-Vlasov SDE living in $\mathbb{R}^d$ in the
reversible case without assuming any type of convexity assumptions for
confinement or interaction potentials. Kramers' type law for the exit-time from
a domain of attraction is established. Namely, in the small-noise regime, the
limit in probability of the first exit-time behaves exponentially. This result
is established using the large deviations principle as well as improved
coupling method.
  Having removed the convexity assumption, this work is a major improvement of
the previously known results for the exit-time problem, the review of which is
provided in the paper.
