The appointing authority of the Chief Minister is the Governor, who suggests a vote of confidence procedurally in the state legislature, to establish the selection of the Chief Minister.
According to the Westminster model of parliamentary system that India follows, the Chief Minister is not elected directly by the people of a state.
The people only elect particular representatives from various constituencies in a state, as members of the state legislature or the Vidhan Sabha (MLAs). These representatives, especially from the majority party which forms the government, then choose the Chief Minister from among them. The tenure of the Chief Minister is for a period of five years, when the state legislative assembly is dissolved and fresh elections are held. However, the tenure of the Chief Minister can be terminated by the governor before the period of five years, when the majority party loses the confidence vote in the state legislative assembly.