We study the interior magnetohydrodynamic structure of a rotating stationary axisymmetric neutron star. We assume the fluid is ideal, infinitely conducting, and flows only azimuthaly. We justify this assumption by considering in detail the superfluid physics in the interior. We obtain some of our results by taking a certain limit of previously discovered magnetohydrodynamic conservation laws. We show that the angular velocity, electric and magnetic potentials, and the red-shifted chemical potential are constant on magnetic surfaces. We demonstrate that the absence of meridional circulation implies the vanishing of the toriodal magnetic field. This clashes with previous arguments from the probable evolution of the magnetic field during the collapse to the neutron star. We solve completely Maxwell's equations for the distribution of magnetic field strength, and we show that the magnetic surfaces are the equipotentials of a simple geometrical invariant. With neglect of gravitational effects the magnetic field must be uniform in the interior in accordance with the Deutsch model, but at variance with numerous other models which have been proposed for ordinary stars. Gravitation causes the magnetic surfaces to flare out toward the polar regions and enhances the central field as compared to the polar field. The star must bemore » charged; the charge distribution depends on the magnetic field strength and on the angular velocity relative to the local inertial frames.« less