In this paper we introduce new domination parameter called efficient complementary perfect triple connected domination number of a graph. A subset S of V of a nontrivial graph G is said to be an efficient complementary perfect triple connected dominating set, if S is a complementary perfect triple connected dominating set and every vertiex is dominated exactly once. The minimum cardinality taken over all efficient complementary perfect triple connected dominating sets is called the efficient complementary perfect triple connected domination number and is denoted by ecpt. We investigate this number for some standard graphs. We also investigate its relationship with other graph theoretical parameters