A same-sex couple in Broken Hill, in far western New South Wales, say they are shocked their daughter has been rejected from a Catholic primary school because of their relationship.

The couple, who do not want to be named, enrolled their daughter into kindergarten at Sacred Heart Primary School for 2012 but say their application was recently rejected.

One of the mothers says the principal phoned her and said the women's relationship and living situation was the reason the application had been turned down.

The women say they welcomed the religious teachings of the school, which would allow their daughter to be "open-minded" to religious beliefs and free to form her own views.

One of the women, who was christened Catholic, says her daughter wanted to attend the same school as her best friend.

The ABC contacted both the school and the Catholic Schools Office but both declined to comment on the decision.