That's a pretty good attempt. The only problem is, the close() method can also throw an SQLException. At least it's declared that way. And yes, you're catching that exception. However if that exception were actually thrown, let's say at line 54 for example, then the PoolManager.returnConnection line would not be executed. So you aren't dealing with it adequately, if you want to be 100% bullet-proof. Even if line 54 threw an exception, you would want to carry on with the rest of the code in the finally-block.
And by the way setting a method's local variable to null is usually pointless, and when you do it immediately before leaving the method, it's always pointless.