PA-34-200 Seneca I
Air Traffic Control Fully Certified
Other / Unknown
ATC Issue All Types; Conflict Airborne Conflict
Air Traffic Control Issued New Clearance
Procedure; Human Factors
ATW has a final approach course for the ILS Runway 3 that rests primarily in our airspace; instead of Green Bay's; so we routinely take point outs for aircraft that they are vectoring to the ILS 3 final approach course.  GRB Approach pointed out an aircraft that was descending out of 12;000 feet about 30 miles East of ATW descending for the final approach to Runway 3. We have a LOA with GRB stating that these aircraft are only allowed to descend to 4;000 feet until they are clear of OSH Tower's airspace. I had a GRB arrival who was about 20 miles South of ATW at 5;000 feet when GRB called for the point out. I started to say; 'Traffic is' and the GRB Controller cuts in and said; 'PA-34?' (who is flashing already in hand off transfer to GRB) I said 'yes' and the GRB Controller said; 'I'll miss him.'  These 2 aircraft were almost 50 miles apart at the time of the point out. I observed GRB descending and vectoring the point out aircraft closer to the final for the ILS 3. I then observed their aircraft descending to 5;000 feet and basically on a collision course with PA-34. I turned PA-34 to a 340 heading to start a turn away from the aircraft. I had no idea what that aircraft was doing so I didn't know exactly what to do. I called GRB and asked them what they were doing with the point out aircraft as PA-34 was right there. I asked if they were descending him further and there was no answer on the land line. I hung up and climbed the PA-34 to 6;000 feet. I waited until I saw the point out aircraft at 4;000 feet then I descended PA-34 back down to 5;000 feet. I told our Supervisor that I was pretty sure GRB just had a loss of separation. Recommendation; GRB should hand off these arrivals to us and we should be working them as they are in our airspace.
MKE Controller described a probable loss of separation event involving GRB's vectors of a Runway 3 ILS arrival.  The reporter suggested these aircraft should be worked by MKE because of the airspace configurations.