  Astrophysical black hole systems are the ideal laboratories for testing
Einstein's theory of gravity in the strong field regime. We have recently
developed a framework which uses the reflection spectrum of black hole systems
to perform precision tests of general relativity by testing the Kerr black hole
hypothesis. In this paper, we analyze XMM-Newton and NuSTAR observations of the
supermassive black hole in the Seyfert 1 galaxy MCG-06-30-15 with our disk
reflection model. We consider the Johannsen metric with the deformation
parameters $\alpha_{13}$ and $\alpha_{22}$, which quantify deviations from the
Kerr metric. For $\alpha_{22} = 0$, we obtain the black hole spin $0.928 < a_*
< 0.983$ and $-0.44 < \alpha_{13} < 0.15$. For $\alpha_{13} = 0$, we obtain
$0.885 < a_* < 0.987$ and $-0.12 < \alpha_{22} < 1.05$. The Kerr solution is
recovered for $\alpha_{13} = \alpha_{22} = 0$. Thus, our results include the
Kerr solution within statistical uncertainties. Systematic uncertainties are
difficult to account for, and we discuss some issues in this regard.
