Magnetohydrodynamic instabilities play an important role in accretion disks systems. Besides the well-known effects of the magnetorotational instability (MRI), the Parker-Rayleigh-Taylor instability (PRTI) also arises as an important mechanism to help in the formation of the coronal region around an accretion disk and in the production of magnetic reconnection events similar to those occurring in the solar corona. In this work, we have performed three-dimensional magnetohydrodynamical (3D-MHD) shearing-box numerical simulations of accretion disks with an initial stratified density distribution and a strong azimuthal magnetic field with a ratio between the thermal and magnetic pressures of the order of unity. This study aimed at verifying the role of these instabilities in driving fast magnetic reconnection in turbulent accretion disk/corona systems. As we expected, the simulations showed an initial formation of large-scale magnetic loops due to the PRTI followed by the development of a nearly steady-state turbulence driven by both instabilities. In this turbulent environment, we have employed an algorithm to identify the presence of current sheets produced by the encounter of magnetic flux ropes of opposite polarity in the turbulent regions of both the corona and the disk. We computed the magnetic reconnection rates in these locations obtaining average reconnection velocities in Alfv\'en speed units of the order of $0.13 \pm 0.09$ in the accretion disk and $0.17 \pm 0.10$ in the coronal region (with mean peak values of order of $0.2$), which are consistent with the predictions of the theory of turbulence-induced fast reconnection.