We define and then study the structural observability for a class of complex networks whose dynamics are governed by the nonlinear balance equations. Although related notions of observability of such complex networks have been studied before and in particular, necessary conditions have been reported to select sensor nodes in order to render a given network observable, there still remain various challenging problems, especially from the systems and control point of view. The reason is partly that sensor node selection problems for nonlinear complex networks have not been studied systematically, which differs greatly from the relatively comprehensive mathematical development for the linear case. In this paper, we are able to construct necessary conditions for the refined structural observability for nonlinear complex networks. For nonlinear balance equations, we further establish a connection between these necessary conditions and the conventional senor node selection method using the structures of the equations.