If the index is local, then its partitions are tied into those of the table and you can't create them separately. You can, however, switch them off and rebuild them separately using syntax such as:

alter index modify partition unusable;

and

alter index rebuild partition part_name;

I've found this quite a useful feature because you can switch off indexes during loads of partitions, which speeds up the loads but doesn't mean you have to rebuild the entire index.