In this work, we study the role of spin-orbit coupling (SOC) in nonradiative relaxation of hot electrons and holes in methylammonium lead perovskite, MAPbI3. For this purpose, we have developed the nonadiabatic molecular dynamics method with two-component spinor wave functions that are solutions of the relativistic Kohn-Sham (KS) equations. We find that SOC enhances contributions of Pb(px) and Pb(py) orbitals to the conduction and valence bands. As a result, the KS orbitals become more sensitive to nuclear motions, leading to the increased nona...