Let \(D\) be a bounded open set in \(\mathbb{C}^ n\) with a \(C^ 2\) boundary \(\partial D\). If a continuous function \(f\) on \(\partial D\) may be continuously extended to \(D\) so that it is holomorphic on \(D\), then \(f\) has the Morera property with respect to every complex hyperplane \(\Lambda\) which meets \(\partial D\) transversely: \[ \int_{\Lambda \cap \partial D}f \alpha=0 \] for each \((n-1\), \(n-2)\)-form \(\alpha\) with constant coefficients. Let \({\mathcal L}\) be an openly connected set of such hyperplanes, containing one that misses \(\overline D\). Let \(\Gamma\) be the trace of \({\mathcal L}\) on \(\partial D\) and let \(f \in C( \Gamma)\) have the Morera property with respect to each \(\Lambda \in \Gamma\). It is proved that \(f\) satisfies then the weak tangential Cauchy-Riemann equations on \(\Gamma\).