Using a unique sample of net domestic product data for districts in India, I investigate the connection between banking sector development, human capital, and economic growth at the sub-national level. Using disaggregate data avoids many of the omitted variable problems that plague cross-country studies of the finance-growth connection and facilitates an instrumentation strategy. The findings show that the growth of many districts in India is financially constrained due to lack of banking sector development, and that the relationship between finance and growth may be non-linear. For the districts in the sample, moving from the 75th percentile of credit/net domestic product to the 25th percentile implies an average loss of 4 percent in growth over the 1990s. This indicates that the gains from increased banking sector outreach may be large. The analysis shows that human capital deepening can reduce the effect of the financial constraint and help decouple growth from financial development. In a district at the 25th literacy percentile, the implied growth loss due to a constrained banking sector is twice as large as in a district at the 75th literacy percentile. Thus, higher levels of human capital may activate alternative growth and production channels that are less finance intensive.