Can my brother kick his girlfriend out legally?

My brother is trying to find an answer to the following. He owns a house and his girlfriend has sporadically lived with him on and off for a couple of years. They have broken up before and gotten back together. He has recently asked her to move out and she basically said that he will have to call the police to get her out as she is not budging. She did put her mailing address as his address and we are all telling him to just pack up her things and change the locks. Can anyone tell me if this girl has a legal leg to stand on? She is not a tenant, she doesn't pay rent...she is just a girlfriend who can't let go and won't leave. What recourse does he have? What should he do to legally get her out of his house?