Let $G=(V,E)$ be a graph, $D\subseteq V$ and $u$ be any vertex in $D$. Then the out degree of $u$ with respect to $D$ denoted by $od_D(u)$, is defined as $od_D(u)=|N(u)\cap (V-D)|$. A subset $D\subseteq V(G)$ is called a near equitable dominating set of $G$ if for every $v\in V-D$ there exists a vertex $u\in D$ such that $u$ is adjacent to $v$ and $|od_D(u)−od_{V-D}(v)|\leq1$. A near equitable dominating set $D$ is said to be a connected near equitable dominating set if the subgraph $\langle D\rangle$ induced by $D$ is connected. The minimum of the cardinality of a connected near equitable dominating set of $G$ is called the connected near equitable domination number and is denoted by $\gamma cne(G)$. In this paper results involving this parameter are found, bounds for $\gamma cne(G)$ are obtained. Connected near equitable domatic partition in a graph $G$ is studied.