We examine the effect of attending private secondary school on educational achievement, as measured by students' scores in a comprehensive standardized math test, in two Indian states: Orissa and Rajasthan. We use propensity score matching (PSM) to control for any systematic differences between students attending private secondary schools and public secondary schools, and assess the sensitivity of our estimates with respect to unobservables using the Rosenbaum bounds. We find that students in private schools in rural (urban) Rajasthan scored about 1.3 (0.4) standard deviation (SD) higher than their counterparts in the public schools. Importantly, the positive private school impact in rural (urban) Rajasthan survives a large (moderate) amount of positive selection on unobservables. We do not find statistically significant difference in urban Orissa, while a positive impact of 0.3 SD in rural Orissa is susceptible to small amount of positive selection on unobservables.