Chief Minister is a designated head of the government of an Indian state. As per Indian Constitution, the Chief Minister is selected by the state Governor.
The parliamentary structure in India chases the Westminster method. Hence the Chief Ministers of Indian states are elected by the members of legislature. The people do not choose the government head; instead they choose their representatives. In turn, the representatives opt for the head of the government.
Nevertheless once the government head is chosen, he enjoys numerous elite executive supremacies. This is in distinction with the state head, the Governor, who is the official head of the state.