This paper studies the spillover effects both within the bond markets for individual U.S. states and between the latter and the market for U.S. Treasury securities. We perform the Forbes and Rigobon (2002) spillover test using daily bond yield data over the period 2005 to 2011. Results are twofold. First, we find that between most markets for individual U.S. state bonds there are negative spillovers. In other words, an increase in borrowing costs in one U.S. state results in better borrowing conditions for other states. Second, we find no substantial spillover effect between shocks originating from state securities and from federal markets, except for a few large issuers. Using causality tests in the frequency domain, we find that the Treasury bond market directly causes changes in the markets for municipal bonds in both the short and long run. There is also some evidence of causality from the municipal to the Treasury bond market, but only of a long-run nature. Our results shed some light on the policy debate on the nature of spillover effects within fiscal unions.