WASHINGTON — The Supreme Court yesterday 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 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 group called 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.

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

The president champions vouchers. And many conservatives who call them a ticket out of dismal and dangerous public schools, while champions of public education, 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.