App to App Single Sign On

I need some help getting app A and app B together where you must be logged into app A and have a value on whitelisted = true to then log you into app B.
Better explanation
App A is the main app and app B is a side app. App B uses information from app A to gain access into app B. If you go to app B and press log-in you must be logged into app A and be whitelisted (true value) which will then use that user in app B and lets you in.

Should I be using API Key or oAuth?