  In this paper, we aim to study the asymptotic behavior for multi-scale
McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit
type theorem, i.e, the deviation between the slow component $X^{\varepsilon}$
and the solution $\bar{X}$ of the averaged equation converges weakly to a
limiting process. More precisely,
$\frac{X^{\varepsilon}-\bar{X}}{\sqrt{\varepsilon}}$ converges weakly in
$C([0,T],\RR^n)$ to the solution of certain distribution dependent stochastic
differential equation, which involves an extra explicit stochastic integral
term. Secondly, in order to estimate the probability of deviations away from
the limiting process, we further investigate the Freidlin-Wentzell's large
deviation principle for multi-scale McKean-Vlasov stochastic system. The main
techniques are based on the Poisson equation for central limit type theorem and
the weak convergence approach for large deviation principle.
