We reduce the problem of the current distribution over the surface of a microstrip dipole in the form of a thin, perfectly conducting strip on a dielectric substrate, which is metalized on one side, to a singular integral equation with the Cauchy kernel. The complex-valued current distributions on the dipole surface are presented along with the dependences of the input impedance on the dipole-arm length normalized to the wavelength for different values of the dielectric permittivity of the substrate.