The issue of return and volatility spillover across the stock markets of different countries has become important as return and volatility shock of one market is transmitted from one market to another in terms of information transmission. Present study using the AR(p) - GARCH(1,1) model has investigated the contemporaneous as well as the dynamic return and volatility spillovers from the US stock markets (represented by NYSE Composite Index) to its Indian counterpart (represented by Sensex) and vice versa. A bi-directional contemporaneous return spillover has been reported while a unidirectional dynamic return spillover from US to India is revealed. However, a bi-directional contemporaneous as well as dynamic volatility spillover effect between the two markets is observed barring in the post-crisis period when no dynamic volatility has been reported from the Indian stock market to US stock market.