Rajeshwari's father, B.M.Shivaramajah, was an advocate in Nanjangud. Her grandmother, Kamalamma Dasappa, was one of the first women graduates in the erstwhile state of Mysore. Rajeswari married Sisir Kumar Chatterjee, a faculty of IISc in 1953. The couple had a daughter Indira Chatterjee, who is now a professor of electrical and biomedical engineering at the University of Nevada, Reno, U.S.