A simple analytical solution is given for a current point source in the vicinity of a thin metallic sheet conductor - which may have polarizable surfaces. The solution is obtained as the limit of a general layered model for a thin intermediate stratum having high conductivity while the thin coating strata have high (complex) resistivities. It is shown that the resulting composite thin sheet can also be treated at the outset employing effective boundary conditions which relate the jump or discontinuity in the tangential electric fields to the normal current flow on the two sides of the sheet. The appropriate discontinuity of the potential is also incorporated into the effective boundary conditions.