Databases work best with regular structures. That's not to say that an inconsistency such as this cannot be accommodated, but it won't be ideal. A lot depends on what do you actually intend to produce out of the data entered.
I would probably opt for a "star" join table of Roles joining Staff (or StaffAssignments) to both Districts and Schools. And if a role can apply to multiple schools in a single district I would consider using a checkbox field to select the applicable schools - provided that it wouldn't conflict with some reporting ability you may want to provide.
Please note that we are discussing an ERD, not the relationships graph. That will be a whole another issue.