The quantum mechanical two Coulomb centers problem for the case of imaginary intercenter parameter and complex conjugate charges is considered. In this case, the Schrodinger equation allows for separation of variables in oblate spheroidal coordinates. Since the potential is defined by the two-sheeted mapping whose singularities are concentrated on a circle, but not points, there arise additional possibilities in choice of boundary conditions. Detailed classification of the various types of boundary-value problems is given. The specific character of the boundary-value problems associated with the quasi-radial equation is discussed. Results of the numerical calculations allowing to draw conclusions about the structure of the energy spectrum are shown.