It depends which bond yields you're talking about. Short-dated bonds and short-term interest rates are substitute goods, and so will move together. If this wasn't the case then an arbitrage opportunity would exist to make a risk-free profit. It's not quite so clear with long-term bond yields; there are a number of issues in play. If short-term interest rates do down, then you might expect there to be an overall downward shift in the bond yield curve, but there are potentially inflationary pressures which are strongest at the long end which makes the result indeterminate.
