  Let $\mathbb{T}$ be the unit circle and $\Gamma\setminus G$ the 3-dimensional
Heisenberg nilmanifold. We prove that the M\"obius function is linearly
disjoint from a class of distal skew products on
$\mathbb{T}\times\Gamma\setminus G$. These results generalize a recent work of
Huang-Liu-Wang.
