"“I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen…” from the Oath of Allegiance "

http://www.newcitizen.us/dual.html

apparently it is not binding:

" the oath has never been enforced to require the actual termination of original citizenship"

http://en.wikipedia.org/wiki/United_States_nationality_law#c...

Edit: can you ask your family if they took that oath, or is the information obsolete? Until now, I thought it was an actual requirement to renounce other citizenships.