Statement I is correct because the Constitution of India explicitly provides circumstances under which a Governor can act in his/her own discretion, notably in appointing the Chief Minister when no party has a clear majority or in the dissolution of the Legislative Assembly (Article 163). In contrast, Statement II is incorrect; the President can reserve a bill for his/her consideration only on the advice of the Governor, as per Article 200. This highlights the degree of constitutional discretion allowed to the Governor in state matters compared to the President's reliance on the state's executive authority.