The Education Department has advised universities that they are required under Title IX to investigate accusations of off-campus rapes of students, specifically citing off-campus fraternity houses. Kansas State recognizes 25 fraternities; all their houses are off campus.

“The fact that the alleged misconduct took place off campus does not relieve the school of its obligation to investigate the complaint,” the department said in a document in 2014 that explains the responsibility of universities to investigate sexual violence. A similar directive was contained in a 2011 letter to universities.

Adele P. Kimmel, a lawyer with the public interest law group Public Justice, said the university’s decision not to investigate complaints of rape at off-campus fraternity houses appeared to directly contravene the Department of Education guidance and also sent a poor message to those off-campus fraternities. “It’s basically saying to fraternities, ‘Just make sure you commit rape at the fraternities and not on campus,’ ” Ms. Kimmel said.

A consultant who advises universities on Title IX issues, Steven J. Healy of Margolis Healy, said: “If the incident involves two students, it’s very likely to create a hostile environment on campus. Therefore the institution would be required to investigate if it knew or should have known.”

Neither Ms. Weckhorst nor Ms. Farmer would agree to be interviewed. In their legal complaints, they express frustration at the university’s unwillingness to investigate their accusations as well as fear of running into the men on campus. Police complaints were filed in both cases.