In order to perform the functions of the program, Live Groups requires access to your Contacts and Address Book. It requires Read access in order to show you your groups and the contacts in each group. It requires Write access to allow you to rename or delete groups, create new groups and add or remove contacts to and from your groups.
All functionality is accessed through the native Android contact provider. Android (or other applications with access) may transmit this data, however none of this data is transmitted or retained off your device by Live Groups or its author.