PHOENIX — Some border county sheriffs want Arizona schools to start asking students whether they are in this country legally.

Pima County Sheriff Clarence Dupnik, who originated the idea, said Arizona taxpayers are underwriting millions of dollars of costs of teaching English to children who have no legal right to be here. He also said there is a link between illegal immigration and social problems and gang activity.

Only thing is, a 1982 U.S. Supreme Court decision appears to make it illegal for school officials to ask. In a 5-4 decision, the justices overturned a Texas law which authorized school district to refuse to enroll anyone who could not prove legal presence in this country.

But Dupnik said it may be time for Arizona to have a test case to put the issue back before the high court to see if the justices still agree.

Dupnik has the backing of Yuma County Sheriff Ralph Ogden and Joe Arpaio, his Maricopa County counterpart. And even Gov. Jan Brewer said she sees no reason that youngsters should not be asked to prove they are U.S. citizens or legal residents.

“When I grew up, when I went to school, when I moved from Nevada to California, I had to bring my birth certificate to prove I was a citizen,’’ she said.

But Attorney General Terry Goddard said he doesn’t think schools have the expertise to determine someone’s legal status.

State School Superintendent Tom Horne he believes the federal government should do a better job of protecting the border.

“But as long as kids are here they should be in school,’’ he said, opposing the idea of finding ways to legally prevent illegal immigrants from getting a public education. “You don’t want them on the street corner.’’

Dupnik, however, has an answer for that: Have schools report their findings to Immigration and Customs Enforcement.

“They would identify the people that are here illegally by the thousands and send them back, kids and parents,’’ he said.

The issue has financial implications: The Pew Hispanic Center estimates that 60,000 to 65,000 of the 1.2 million youngsters in Arizona schools are not in this country legally.

The Department of Education figures basic state aid for students is about $6,000 a year, not counting what the state pays for school construction. That puts the price tag approaching $390 million.

That doesn’t count the extra $360 per student Arizona now gives to schools to help “English language learners,’’ students who come to school not proficient in the language. Assuming two thirds of these youngsters fit that category, that adds another $15 million to the tab.

In 1982, however, the Supreme Court voided a 1975 Texas law which denies state aid to districts for children not “legally admitted’’ into the United States. That law also allowed districts to deny admission to those students.

Attorneys for Texas argued that the 14th Amendment to the U.S. Constitution, which entitles all persons to equal protection of law, does not apply to those not in the country legally.

“We reject this argument,’’ wrote Justice William Brennan for the majority. “Whatever his status under the immigration laws, an alien is surely a ‘person’ in any ordinary sense of the term.’’

And Brennan said education is the only way people can advance themselves.

“Such an opportunity, where the state has undertaken to provide it, is a right which must be made available to all on equal terms.’’

Ogden said all that ignores the financial burden being placed on the residents of Arizona and other border states.

“I’m paying for my kids and your kids to go to school who are citizens,’’ he said. Ogden said he would support taking another case to the high court, and not only over the issue of education funding.

“Some of those same families would be collecting other social services from us,’’ he said.

Arpaio said schools should not be able to decide they don’t want to weed out those who are not here legally.

“We need every element of society to assist in resolving this problem, whether it’s in the school or anywhere else,’’ he said.

But Santa Cruz County Sheriff Tony Estrada said schools should not be in the business of asking students their immigration status.

“You’re involving school officials in the immigration process,’’ he said. And Estrada said he sees that as a first step toward having other state and local public employees also doing the same thing, including his own officers.

“We can’t afford it,’’ he said.

Ogden, who has been involved in law enforcement along the border for more than 41 years, said that shift in costs already is occurring.

He said federal agents used to take care of situations where deputies picked up someone crossing the border illegally or retrieving drugs that had been thrown over the fence. They also prosecuted those cases

“All of a sudden, we got blindsided,’’ Ogden said. “Everything we caught coming over the border with drugs was on our dime.’’

The Pew report estimates there are another 100,000 to 110,000 youngsters in Arizona schools who are the children of illegal immigrants but were born in this country. That makes them citizens who would be unaffected by any reversal of that 1982 Supreme Court ruling.

Even if Arizona is successful in convincing the high court to overturn its 1982 decision, that may not end the debate.

Four years earlier, Attorney General Jack LaSota issued a formal legal opinion saying the only inquiry school officials can make of parents who want to enroll their children is whether a they are Arizona residents.

“The children of many ‘illegal aliens’ are born in the United States and are, therefore, citizens,’’ LaSota wrote. “Inquiry into the ‘illegal alien’ status could result in the intimidation of the parents, jeopardize the paramount objective of educating their children and therefore be improper.’’