New York State's education department is investigating a complaint that the policy at Cornell University of reserving halls of residence for members of racial groups violates the law. The complaint was lodged by the local Civil Rights Coalition.

For years the Ivy League university in Ithaca has had a dormitory called Ujamaa mainly for black students. It recently opened others for American Indians and Spanish-speaking students.

Late last year the coalition complained that the dormitories fostered racial segregation. It asked the state to examine whether the halls of residence broke university regulations that prohibit discrimination on grounds of race or ethnicity.

The state of New York's education department is looking at whether Cornell has effectively encouraged racial separation and why students are housed.

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The Ujamaa dormitory was set up after an armed takeover of the main student union in 1969 by black students who said the university was not meeting their needs. New York state's education department examined Ujamaa in the mid-1970s and decided that the dormitory could continue because Cornell promised to make sure admission was not based on race. Of the 140 students living in Ujamaa, three are white.

Similarly the university has tried to ensure that its Native American and Hispanic living units have been open to students from other races. When it opened its Native American dorm, the university said it wanted half the students to be indian and the rest from other ethnic backgrounds.

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Two years ago Cornell's president was under pressure to create a living unit for gay students, but he refused.