The app will need permission for the following:
a) access contacts - so that you can dial from your contacts, or add someone to them from the app
b) network access (wifi & mobile) - so that the call can progress over a data bearer on an available technology. They may abuse this by also bundling enhanced purchasing suggestions in informative sub-windows of the app
c) at a stretch, location, but this should really be looked after by the mobile network infrastructure
To offer a more complete solution, it may ask to be able to receive and send SMS/MMS, use the camera (particularly if video calls are supported), and store media files. Potentially, to guarantee access to 911 facilities, it may require the ability to make a phone call (via cellular).