Let G = (V, E) be a graph with chromatic number ${chi}(G)$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every ${chi}$-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ${gamma}_{ct}$(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.