Let \(\overline M(\varphi, \xi, \eta, g)\) be a \((2+ 1)\)-dimensional trans-Sasakian manifold [see \textit{J. A. Oubina}, Publ. Math. 32, 187-193 (1985; Zbl 0611.53032)]. A submanifold \(M\) of \(M\) is said to be generic if the dimension of the subspaces \({\mathcal D}_x= T_x M\cap \varphi T_x M\), \(x\in M\), is constant along \(M\); thus \({\mathcal D}: M\ni x\mapsto {\mathcal D}_x\) is a differentiable distribution on \(M\). Let \(M\) be a generic submanifold of \(\overline M\). The authors study the integrability problem of the distributions \(\mathcal D\), \({\mathcal D}\oplus \{\xi\}\), \({\mathcal D}^\perp\) and \({\mathcal D}^\perp\oplus \{0\}\). They find also analytic conditions for the leaves of \({\mathcal D}\oplus \{\xi\}\) and \({\mathcal D}^\perp\) to be totally geodesic in case they are integrable. Moreover, it is proved that a generic submanifold of a trans-Sasakian manifold is a Cauchy-Riemann manifold.