The NMR relaxation rate is studied on the magnetic states of an impurity in bilayer graphene within a tight-binding scenario. The dependencies of the relaxation rate on temperature, interlayer interaction and also the chemical potential have been considered. Although for low temperatures we observe the usual Korringa relation, a characteristic of the conventional fermions, the rate increases with the increase in temperature and tends to saturate for high temperatures. For small interlayer interactions (t⊥) the system can be either magnetic or non-magnetic. However for higher t⊥ we observe the existence of only a pure magnetic state. In graphene this transition is also observed with two cusps related to the magnetic to non-magnetic transition, which modifies to a single hump for higher t⊥, where the system is purely magnetic for any value of chemical potential.