Overhanging Branch - Restart ...

I want to ask how fellow referees deal with a ball striking a overhanging branch.

I've done games where referees tell me that since the branch is part of the field, play should continue. Then others tell me you should blow the whistle to stop the match and restart with a drop ball. Yet some others say that if the ball was in the process of going out of bounds anyway, it should be a throw-in.

Please help. I just want to do the restart right.