The object of the Butler Committee of 1927 was to

Correct Option: improve the relationship between the Government of India and the Indian States.

Explanation:
The Indian States Committee, popularly known as the Butler Committee, was appointed in 1927 under the chairmanship of Sir Harcourt Butler. Its primary objective was to examine and define the nature of the relationship between the Paramount Power (the British Crown / Government of India) and the rulers of the Indian Princely States.

Key details regarding the Butler Committee (1927):
• Objective: To investigate the financial and economic relations between British India and the Native States, and to recommend steps for improving their relationship.
• Key Recommendation: The committee stated that "Paramountcy must remain paramount" and emphasized that the princely states should not be handed over to an Indian Government responsible to an Indian Legislature without their prior consent.