OXFORD, Miss. — The University of Mississippi said Friday that students could face criminal charges for placing a noose on a statue honoring the college’s first black student, and a fraternity announced that it had expelled three men because of the incident.

Sigma Phi Epsilon, a social fraternity on campus, said in a statement that the men were a part of the group’s chapter at the university. The chapter, which said it told investigators about the role its members may have played in the vandalism, was suspended.

The university said its inquiry led law enforcement officials to seek interviews with three students, all of them white 19-year-old freshmen from Georgia. But the students, whom the university did not identify because of an educational privacy law, refused through their lawyers to meet with the authorities unless investigators secured arrest warrants.

The university said that two of the students initially agreed to meet with law enforcement officials on Thursday morning, but that neither appeared.