Kazi Nazrul Islam born as a British-Indian. At his time of birth to 1947, there was no difference between a Bangladeshi and an Indian - as none of those countries existed. He naturally became an Indian citizen after the independence of India.
Unfortunately, his health deteriorated in the late ‘40s, and he was in intensive care in most part of his later life. After the independence of Bangladesh, he was invited to the country with the permission of Indian government, and he he was accorded the citizenship of Bangladesh. He died and buried in Dhaka in 1976.
To answer the question, Nazrul’s poetry is not property of a single country, and poets like him do not have nationality. Nazrul is equally Indian, and Bangladeshi.