I want to calculated the statistical uncertainty for the sum of AAAA->Add(BBBB).
By default, I used the sumw2(). I know sumw2 is only correct to two independent histograms.
So, how will I do? It is better if give a corresponding example.

In this case you will have to compute the resulting bin uncertainties yourself, using the obtained values from GetBinError() of the two histograms and the known correlation using for example the standard formula of correlated error propagation, for example from