Not sure I understand your question correctly. You don't have location type data at the district level, so you can't show it like that. You could perform a statistical analysis - average, sum, count, etc. - of your local data aggregated at the district level, which I'd put in a third shapefile or feature class, but you can't do it directly. You may also have to do some apportioning if local areas can be in more than one district. Or am I misunderstanding your question?
