The characteristics of an Avadhuta Yogi are mentioned in the Chapter 6 of Siddha Siddhanta Paddhati by Gorakhnath. Here are the qualities of an Avadhuta:
He is well versed in the discipline of Yoga.
What he speaks is the revealed word.
Whatever place he visits becomes a tirtha (place of pilgrimage).
Though he undergoes phases of tyaga (abandonment) and bhoga (enjoyment), he is indifferent to both.
An Avadhuta is the follower of the divine path and nothing surpasses his divinity.