This paper empirically investigates the short run dynamic linkages between NSE Nifty in India and NASDAQ Composite in US during the recent 1999-2001 period using intra-daily data, which determine the daytime and overnight returns. The study carries out a comprehensive analysis from correlation to Granger causality and then to application of GARCH models to examine the co movement and volatility transmission between US and Indian stock markets. Specifically, the study employs a two stage GARCH model and an ARMA-GARCH model to capture the mechanism by which NASDAQ Composite daytime returns and volatility have an impact on not only the mean but also on the conditional volatility of Nifty overnight returns. It is found that the simple ARMA-GARCH model performs better than the more complex Two-stage GARCH model, described in the literature. The main findings of this study are as follows: First, the granger causality results indicate unidirectional granger causality running from the US stock markets (both NASDAQ Composite and S & P 500 indices) to the Indian stock market, NSE Nifty index. Second, the previous daytime returns of both NASDAQ Composite and NSE Nifty have significant impact on the NSE Nifty overnight returns. However, the volatility spillover effects are significant only from NASDAQ Composite implying that the conditional volatility of Nifty overnight returns is imported from US. We found that on an average the effect of NASDAQ daytime return volatility shocks on Nifty overnight return volatility is 9.5% and that of Nifty daytime return is a mere 0.5%. In out of sample forecasts, however, we found that by including the information revealed by NASDAQ day trading provides only better forecasts of the level of Nifty overnight returns but not its volatility.