The CEO is appointed by the state government. - This statement is incorrect.
As per the electoral system in India, the Chief Electoral Officer is appointed by the Election Commission of India and not by the state government.
This is clearly mentioned in the given note that "The Chief Electoral Officer is appointed by the Central Election Commission".
The CEO works under the supervision of the Election Commission of India. - This statement is correct.
The CEO acts as the representative of the Central Election Commission in the state and works under its supervision and direction.
The CEO helps in implementing the decisions of the Election Commission at the state level.
The CEO has the power to conduct elections to local bodies. - This statement is incorrect.
Elections to local bodies do not come under the jurisdiction of the CEO but under the jurisdiction of the State Election Commission (SEC).
As mentioned in the notes, the State Election Commission came into existence on 3 December 1993 and is responsible for supervising the elections to local bodies.
The CEO mainly helps in conducting elections to the Parliament and State Assemblies.