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An Alabama superintendent is denying allegations that a fifth-grade teacher and a librarian distributed Bibles during class at a public school, saying the claims are either "inaccurate or false."

Limestone County School District Superintendent Barry Carroll said he received a letter Tuesday from the American Civil Liberties Union in Alabama regarding a parent of two students at Blue Springs Elementary who said the Bibles were doled out within the past three months on multiple occasions.

"Based on what I hear from the teachers, the accusations are inaccurate, if not false," Carroll told FoxNews.com. "We live in the Bible Belt, so children from time to time come in and ask if there's a Bible they can have."

Carroll said the school district allows materials, including Bibles, to be placed on a designated table where students can pick up literature as they choose. He also denied accusations that another fifth-grade teacher, Jody Brown, taught creationism when the topic of evolution arose in a science lesson.

"There's no attempt here to go above the law," Carroll said. "We, as employees of the state, have a responsibility to uphold state law. We're not going to intentionally step out of bounds with that."

Carroll said he asked Brown, teacher Amanda Moss and the school's librarian, Diane Gilliam, who allegedly distributed Bibles to first- and second-grade students, to provide their account of events in writing. The findings of an internal investigation will be submitted to the school district's attorney, he said.

"We don't wind [students] up or pass out Bibles," Carroll continued. "But if there was an error -- and I don't think there was -- we will address it."

Thomas Moore, the parent of two students at the school, notified ACLU officials of the alleged practices, which violate the First Amendment of the U.S. Constitution.

"In one instance, a fifth-grade teacher [Moss] went from classroom to classroom and placed a stack of Bibles on a desk in each room and instructed students to 'come get it' if they wanted one," the ACLU's letter read. "On another occasion, first-grade and second-grade students took a special trip to the library, where the librarian [Gilliam] handed out Bibles to students."

The letter continued, "Unsurprisingly, with the rest of their classmates looking on, Mr. Moore's children felt uncomfortable refusing the Bibles and thus, like others in the class, accepted them at the behest of their teachers."

Allison Neal, legal director of the ACLU's Alabama chapter, said the religious development of children should be guided by families and faith communities rather than by public school officials.

"Religious liberty is a fundamental freedom guaranteed by the Bill of Rights and is best protected when the government stays out of religion," Neal said in a statement.

And while creationism may be taught in a variety of classes, including history, religious studies or cultural studies, Neal said federal courts have repeatedly struck down attempts to teach creationism in public school science classes.

Brown recently refused to continue an evolution lesson in a science class, saying, "some of us believe in God" and "some of us believe that the world was made in seven days and that God created man and the trees," according to the ACLU's letter to Carroll.

"Ms. Brown's practice of teaching or otherwise promoting creationism is, simply put, unlawful," the letter continued. "As the district is surely aware, the federal courts have been unequivocally clear that efforts to inject religious beliefs regarding the origin of life into public school science curricula are constitutionally impermissible, no matter what form they take."

ACLU officials have requested a response to the March 22 letter within 14 days.

Michael Sibley, director of communications for the Alabama Department of Education, said the onus concerning most issues surrounding teaching practices goes back to the local school system.

"We strongly discourage school systems from teaching any religion in any context other than literature and/or history," Sibley said in an email to FoxNews.com. "Two text books have been approved by the State Board of Education, 'The Bible in History and Literature' and 'The Bible and its Influence' for use in the aforementioned context."

In regards to creationism, Sibley said the Alabama Course of Study does not address it individually.

"The Alabama Course of Study deals with Theories of Evolution," Sibley's email continued. "Creationism is one of those theories. The Alabama Course of Study presents each of these so that students can draw their own conclusion for themselves."