On a star-shaped bounded domain \(\Omega\), the authors study semi-linear boundary value problems of the type: \( -\Delta_{H} u = g(u)\) in \(\Omega \) and \( u=0\) in \( \partial \Omega\), where \(\Delta_{H}\) is the sub-Laplacian of the Heisenberg group and \(g\) is a \( C^{1}\) function in \(\Omega\). After presenting some preliminary results, thea give the CR Pohožaev identity and prove the nonexistence of positive solutions of the above mentioned problem. A Yamabe-like problem is also studied.