  While the Kerr-Schild double copy of the Coulomb solution in dimensions
higher than three is the Schwarzschild black hole, it is known that it should
be a non-vacuum solution in three dimensions. We show that the static black
hole solution of Einstein-Maxwell theory (with one ghost sign in the action) is
the double copy with the correct Newtonian limit, which provides an improvement
over the previous construction with a free scalar field that does not vanish at
infinity. By considering a negative cosmological constant, we also study the
charged Ba\~nados-Teitelboim-Zanelli black hole and find that the single copy
gauge field is the Coulomb solution modified by a term which describes an
electric field linearly increasing with the radial coordinate, which is the
usual behaviour of the Schwarzschild-AdS black hole in higher dimensions when
written around a flat background metric.
