  The paper is devoted to studying the asymptotics of the family
$(\mu^\varepsilon)$ of stationary measures of the Markov process generated by
the flow of stochastic 2D Navier-Stokes equation with smooth white noise. By
using the large deviations techniques, we prove that this family is
exponentially tight in $H^{1-\gamma}(D)$ for any $\gamma>0$ and vanishes
exponentially outside any neighborhood of the set $\cal O$ of $\omega$-limit
points of the deterministic equation. In particular, any of its weak limits is
concentrated on the closure $\bar{\cal O}$. A key ingredient of the proof is a
new formula that allows to recover the stationary measure $\mu$ of a Markov
process with good mixing properties, knowing only some local information about
$\mu$. In the case of trivial limiting dynamics, our result implies that the
family $(\mu^\varepsilon)$ obeys the large deviations principle.
