  General point interactions for the second derivative operator in one
dimension are studied. In particular, ${\mathcal P \mathcal T}$-self-adjoint
point interactions with the support at the origin and at points $\pm l$ are
considered. The spectrum of such non-Hermitian operators is investigated and
conditions when the spectrum is pure real are presented. The results are
compared with those for standard self-adjoint point interactions.
