  For a nilmanifold $G/\Gamma$, a $1$-Lipschitz continuous function $F$ and the
M\"obius sequence $\mu(n)$, we prove a bound on the decay of the averaged short
interval correlation $$\frac1{HN}\sum_{n\leq N}\Big|\sum_{h\leq H}
\mu(n+h)F(g^{n+h}x)\Big|$$ as $H,N\to\infty$. The bound is uniform in $g\in G$,
$x\in G/\Gamma$ and $F$.
