Rajshree is the daughter of acclaimed Indian filmmaker V. Shantaram and actress Jayshree, second wife of V. Shantaram. Her brother Kiran Shantaram was a former Sheriff of Mumbai.
While shooting with Raj Kapoor in America for the film Around the World in 8 Dollars, she met American student Greg Chapman. The two married three years later in a Vedic, Hindu marriage ceremony in India, that lasted five days and was attended by 15,000 guests. She went with her husband to permanently live in America. They have one daughter Chandrika. Chapman changed his name to Gautam. They live in Los Angeles.