  This paper deals with a stochastic recursive optimal control problem, where
the diffusion coefficient depends on the control variable and the control
domain is not necessarily convex. We focus on the connection between the
general maximum principle and the dynamic programming principle for such
control problem without the assumption that the value is smooth enough, the set
inclusions among the sub- and super-jets of the value function and the
first-order and second-order adjoint processes as well as the generalized
Hamiltonian function are established. Moreover, by comparing these results with
the classical ones in Yong and Zhou [{\em Stochastic Controls: Hamiltonian
Systems and HJB Equations, Springer-Verlag, New York, 1999}], it is natural to
obtain the first- and second-order adjoint equations of Hu [{\em Direct method
on stochastic maximum principle for optimization with recursive utilities,
arXiv:1507.03567v1 [math.OC], 13 Jul. 2015}].
