By modifying the heuristic principle in several complex variables obtained by \textit{G. Aladro} and \textit{S. G. Krantz} [J. Math. Anal. Appl. 161, 1-8 (1991; Zbl 0749.32001)], the author proves some normality criteria for families of holomorphic mappings of a domain \(D\subset \mathbb{C}^n\) into the complex \(N\)-dimensional projective space \(\mathbb{P}^N(\mathbb{C})\) related to the Green's and Nochka's Picard type theorems. The equivalence of normality to being uniformly Montel at a point is obtained: Let \(F\) be a family of holomorphic mappings of a domain \(D\subset \mathbb{C}^N\) into \(\mathbb P^N(\mathbb C).\) Then \(F\) is normal at a point \(z_0\in D\) iff \(F\) is uniformly Montel at the point \(z_0.\) Two examples are included to illustrate the author's theory.