This is what I would start with IF I was a detective.
1. Phone records for the past 3 to 6 months. Interview every person, they must of been in contact with the intruder.
2. Bank records. Any unusual deposits for large amounts. Interview for the same.
3. Visit the places they did volunteer work and ask questions. You never know, something might pop up.
4. Ask relatives how were their relationship with ALL family members. No one is perfect and I am sure someone did not get along etc. Look at the signs when you interview them. If they hesitate or don't look you in the eye to answer a question. RED FLAG.
Just my thoughts................................