The Constitutional Advisor to the Constituent Assembly of India was Sir B.N. Rao. He played a crucial role in providing legal and constitutional expertise during the drafting of the Indian Constitution.

Option 1, Dr. Rajendra Prasad, was the first President of India and not the Constitutional Advisor. Option 2, Dr. B.R. Ambedkar, was the Chairman of the Drafting Committee and one of the principal architects of the Indian Constitution, but he was not the Constitutional Advisor.

Option 4, Shri K.M. Munshi, was a prominent member of the Constituent Assembly and played a significant role in the drafting process, but he did not serve as the Constitutional Advisor.

Therefore, the correct answer is option 3, Sir B.N. Rao.