We consider a stationary linear AR($p$) model with observations subject to gross errors (outliers). The autoregression parameters as well as the distribution function (d.f.) $G$ of innovations are unknown. The distribution of outliers $Π$ is unknown and arbitrary, their intensity is $γn^{-1/2}$ with an unknown $γ$, $n$ is the sample size. We test the hypothesis for normality of innovations $$\mathbf{H}_Φ\colon G \in \{Φ(x/θ),\,θ>0\},$$ $Φ(x)$ is the d.f. $\mathbf{N}(0,1)$. Our test is the special symmetrized Pearson's type test. We find the power of this test under local alternatives $$\mathbf{H}_{1n}(ρ)\colon G(x)=A_n(x):=(1-ρn^{-1/2})Φ(x/θ_0)+ρn^{-1/2}H(x), $$ $ρ\geq 0,\,θ_0$ is the unknown (under $\mathbf{H}_Φ$) variance of innovations. First of all we estimate the autoregression parameters and then using the residuals from the estimated autoregression we construct a kind of empirical distribution function (r.e.d.f.), which is a counterpart of the (inaccessible) e.d.f. of the autoregression innovations. After this we construct the symmetrized variant r.e.d.f. Our test statistic is the functional from symmetrized r.e.d.f. We obtain a stochastic expansion of this symmetrized r.e.d.f. under $\mathbf{H}_{1n}(ρ)$ , which enables us to investigate our test. We establish qualitative robustness of this test in terms of uniform equicontinuity of the limiting power (as functions of $γ,ρ$ and $Π$) with respect to $γ$ in a neighborhood of $γ=0$.