The three students live in Glenburn, Orrington and Palermo.
These towns do not operate their own public high schools, allowing the students to go elsewhere.
The Institute of Justice is representing the students, saying they should be allowed to attend the school of their choice, with their tuition paid.
However, the ACLU argues it violates the separation of church and state.
"Everybody has a right to practice their religion but they don't have the right to have the government to pay for religious activities," Zachary Heiden of ACLU of Maine said.
"Here, people are challenging Maine's law, saying they want the government to fund religious activities," Heiden said.
Tim Keller of the Institute of Justice had a different view.
"The clients are confident that they are in the right here and that they will ultimately prevail in this case," he said.
A judge will rule on whether the ACLU can be involved by the end of the month.
The ruling on the students is expected to be made in January.