This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
You could perhaps use javap to disassemble the classes. This might enable you to find classes where the Connection.close method was not called. But just because a class contains a call to Connection.close, that doesn't mean the call is actually executed reliably and correctly at run time. There isn't any automated way to determine that.
So you might be better off just doing a source-code search to identify the classes where connections are created, then have a person look at each of those classes.