A: 

I'm not sure I understand your question fully, so please clarify if necessary.

If you want to query the cube to get persons by state, you should add a Referenced relationship between Person and State, using Case as the Intermediate dimension.

  1. Select the empty box at the intersection of Person and State and click on the button
  2. Select Referenced from the relationship type dropdown
  3. Select Case as the Intermediate dimension
  4. Selecting the matching attributes in the two attribute dropdowns
  5. Click OK.

Deploy and process the cube, and it should work the way you want. Then you can get rid of the (State - Person) dimension.

Dave Bauman
You are correct in what I want to do, but wouldn't I be recreating yet another state-person dimension? I tried referenced dimensions, and that's what happend. Maybe my expectations is just wrong. If I work with a cube that has multiple measure groups from different tables, I would want a dimension to appear only once, so that you don't have to know which one is the right one for a particular query.
cdonner
You want to be able to generate a query something like this? The State dimension, and for each State, a count of Cases and a count of Persons. You need a single dimension so you can compare multiple measures side-by-side. I don't know why this didn't work when you tried it. You don't want the State-Person dimension you have now, indicated by the green line. Try deleting that dimension and then setting up the referenced dimension.
Dave Bauman
A: 

If the Person table contains the key for the State dimesion it should be as simple as setting up a regular relationship between the State dimension and the Person measure group. there should be no need to create referenced or fact relationships.

Darren Gosbell