Almost half of people surveyed feel that Muslim students should be allowed to wear hijabs or headscarves in State schools.
According to a new TNS/mrbi poll in today's Irish Times, people are also divided on whether the Government should provide guidelines on the matter to State schools.
Some 48% of those surveyed last week for the poll felt Muslim students should be allowed to wear hijabs in State schools, while 49% believed that the Government should provide the schools with guidelines.
39% of people felt students should not be allowed to wear any Muslim headdress.
Four out of ten of those surveyed across the country last week felt that the Government should not get involved in the issue.
Just over one in ten people had no opinion on the matter.
The poll found that women were more likely to agree with the wearing of hijab, but there was little difference between those questioned in rural and urban areas.
Minister for Education Batt O'Keeffe said recently that the Government would consider whether to issue guidelines when it drafts an intercultural education strategy later in the year.