WASHINGTON — The Supreme Court today refused to take up the issue of school choice in Maine, where a state law bars the use of public funds to send students to private religious schools.

The case, Anderson v. Durham School Department, could have provided a platform for a court battle over school choice and the separation of church and state.

In Maine, school districts in 145 small towns with no high schools offer tuition for 17,000 students to attend high schools of their choice, public or private, in-state or out-of-state. But religious schools are no longer on the list.

Asking the Court to take the case, a conservative group, the Institute for Justice, is representing eight Maine families who would receive public tuition funds but for the fact that their children attend religious schools.

Florida Gov. Jeb Bush and President Bush’s homestate of Texas weighed in, saying in filings to the Supreme Court that the state of Maine is unconstitutionally discriminating against religion.

Vouchers are championed by the president and many conservatives who call them a ticket out of dismal and dangerous public schools. Champions of public education, meanwhile, say that vouchers divert already-scarce resources from a system badly in need of repair.

Last April, the Maine Supreme Judicial Court ruled that restrictions on tuition vouchers are a valid, constitutional enactment. The court said the state attorney general and the Legislature were motivated by a desire to respect and comply with the Constitution rather than any religious hostility.

The Maine court relied on the U.S. Supreme Court’s 2004 ruling in Locke v. Davey, which upheld a Washington state college scholarship program prohibiting the use of scholarship funds for pursuit of a devotional theology degree.

The Institute for Justice said the Maine case would give the justices an opportunity to make clear that its 2004 decision only carved out a narrow exception to the general rule requiring equal treatment of religious and nonreligious options.

The state of Maine’s tuition system goes back to 1879 when nearly all private schools in the state were religious.

In 1980, the state attorney general said the program violated the U.S. Constitution’s establishment clause. The Maine Legislature made it law in 1983.

In asking the Supreme Court to take the case, the Maine families cited the Court’s 2002 decision in Zelman v. Simmons-Harris, which allowed the use of public funds in inner-city Cleveland to underwrite tuition at private or parochial schools if parents retain a wide choice of where to send their children.