onConnectionFailed giving SIGN_IN_REQUIRED(4)

I had the same problem.

From documentation:
The client may choose to continue without using the API or it may call startResolutionForResult(Activity, int) to prompt the user to sign in.

So you should try to sign in by using startResolutionForResult() function

@Override
public void onConnectionFailed(ConnectionResult result) {
   if (result.hasResolution()) {
       try {
           // !!!
           result.startResolutionForResult(this, REQUEST_CODE_RESOLVE_ERR);
       } catch (SendIntentException e) {
           mPlusClient.connect();
       }
   }

   mConnectionResult = result;
}