Relativistic reflection features in the X-ray spectra of black hole binaries and AGNs are thought to be produced through illumination of a cold accretion disk by a hot corona. In this work, we assume that the corona has the shape of an infinitesimally thin disk with its central axis the same as the rotational axis of the black hole. The corona can either be static or corotate with the accretion disk. We calculate the disks emissivity profiles and iron line shapes for a set of coronal radii and heights. We incorporate these emissivity profiles into RELXILL_NK and we simulate some observations of a black hole binary with NuSTAR to study the impact of a disk-like coronal geometry on the measurement of the properties of the system and, in particular, on the possibility of testing the Kerr nature of the source. We find that with a disk-like corona it becomes difficult, in general, to constrain the geometric properties of the black hole spacetime, while the astrophysical properties of the accretion disk are still well recovered.
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