Statement I is correct: Marsupials, which are a type of mammal characterised by the presence of a pouch (marsupium) for carrying their young, are not naturally found in India. Marsupials are primarily native to the Americas and Australia. 

Statement II is incorrect: Marsupials can thrive in a variety of habitats, not just montane grasslands without predators. Many marsupial species are found in a wide range of ecosystems, including forests, savannas, and even urban areas, and can coexist with a variety of predators. Therefore, the correct answer is: Statement-I is correct, and Statement II is incorrect.