I introduce myself and tell them why I am calling. I have had situations where the reference has offered a “narrative” while others wanted me to ask questions.
One thing you may want to do is to call people who you know in that neighborhood and ask if they know the family. You may get better information then from the “official references”.
I know someone who called a member of his family and only asked if he knew “Ploni” and the person responded “what a sweet boy”. Only then was he told that the caller was checking on “Ploni” as a potential shidduch for his daughter.