A general Sommerfeld integral formulation is given for the electromagnetic (EM) fields of an oscillating vertical Magnetic or electric dipole over an electrically inhomogeneous thin sheet. The electrical properties of the sheet are characterized by a conductance function that is an arbitrary function of spatial coordinates. When the conductance function has axial symmetry relative to the source dipole, the general solution form simplifies to a Fredholm integral equation of the third kind. The gereral solution is shown to reduce to the special case of an infinite sheet having uniform conductance. When the sheet conductance is either uniform or varies linearly, the field expressions show an algebraic dependence on the conductance. For a general inhomogeneous conductance distribution, the field dependence is not algebraic.