  Given the pair of vector fields $X=\partial_x+|z|^{2m}y\partial_t$ and $
Y=\partial_y-|z|^{2m}x \partial_t,$ where $(x,y,t)=
(z,t)\in\mathbb{R}^3=\mathbb{C}\times\mathbb{R}$, we give a condition on a
bounded domain $\Omega\subset\mathbb{R}^3$ which ensures that $\Omega$ is an
$(\epsilon,\delta)$-domain for the Carnot-Carath\'eodory metric. We also
analyze the Ahlfors regularity of the natural surface measure induced at the
boundary by the vector fields.
