Spec indicates :

9.6.4.1 Connection.close
An application calls the method Connection.close() to indicate that it has
finished using a connection. All Statement objects created from a given
Connection object will be closed when the close method for the Connection
object is called.
Once a Connection has been closed, any attempt to access any of its methods with
the exception of the close(), isClosed() or isValid() methods will result in
a SQLException being thrown.

problem is that after closing a connection, using a statement isClosed might not return the expected True value.