Step 1: Understanding the Task
We need to evaluate each statement about the office of the Chief Minister in India and identify the one that is factually incorrect according to the Constitution.
Step 2: Evaluating Each Statement
(A) A person who is not a member of the state legislature cannot be appointed as Chief Minister: This statement is INCORRECT. Article 164(4) of the Constitution allows a person who is not a member of the state legislature to be appointed as a Chief Minister (or any other minister). However, they must become a member of either House of the state legislature within six months of their appointment, failing which they cease to be a minister.
(B) Chief Minister is appointed by the Governor: This statement is CORRECT. According to Article 164(1), the Chief Minister shall be appointed by the Governor.
(C) The position of the Chief Minister at the state level is analogous to the position of Prime Minister at the Centre: This statement is CORRECT. Both are the heads of their respective councils of ministers and are the de facto executive heads of the government at the state and central levels, respectively.
(D) Chief Minister may be a member of any of the two Houses of a state legislature: This statement is CORRECT. In states with a bicameral legislature, the Chief Minister can be a member of either the Legislative Assembly (lower house) or the Legislative Council (upper house).
Step 3: Final Answer
The question asks for the INCORRECT statement. Statement (A) is factually incorrect. Therefore, option (A) is the correct answer.