The organization says it has grave constitutional and statutory concerns about Davis School District's decision.
The picture book "In Our Mothers' House" tells the story of three adopted children growing up with two mothers.
The district requires parents to sign a permission slip before students can check out the book, citing state law which prohibits advocacy of homosexuality in its curriculum.
The ACLU of Utah also is seeking public records detailing the decision to restrict the book and any others in school libraries.
The ACLU has said the First Amendment protects student access to books.
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