Let $G=(V,E)$ be a connected graph of order $P(G)\geq 2$. The connected detour number of $G$, denoted $cdn(G)$, is introduced and studied by A. P. Santhakumaran and S. Athisayanathan [7]. In this paper, we characterize connected graph $G$ of $cdn(G)=2$ and of detour diameter $D(G)=5,6$.