The Dominion of India existed as a transitory interim government formed after the formal declaration of Indian independence on 15 August 1947 which lasted until the enforcement of the Indian Constitution on 26 August 1950, which made India a republic ( Republic of India ). Until the adoption of the Constitution, India remained in a state similar to other Dominions such as Canada, Australia and New Zealand, and even had Lord Mountbatten serve as a Governor-General ( who acted as a representative of the British Crown ). This government allowed the governance of India until the basic shape of the new Independent India in the form of a Constitution and republican institutions could be formed and adopted, as well as allow the integration of the Princely States into India. While the Indian independence movement has a long history, the formal process itself was peaceful.
The United States of America, on the other hand, won its independence through a war ( the Revolutionary War ). Therefore, no transitory government under the British Empire was formed for the purpose of governing America until a Constitution ( the Articles of Confederation in this case, since the American Constitution was adopted later ) was formed, adopted and enforced.
EDIT: Peaceful here refers to vis a vis the overlord ( Britain in both cases ). The dissolution of the British Raj was marred by violence due to the Partition, forced annexation of Junagarh and Hyderabad, as well as the First Indo-Pakistani war fought over Jammu and Kashmir.