PHOENIX — Republican lawmakers voted Tuesday to make an end-run around the budget and shift around some money to fund public and private school vouchers for some students.

On an 8-3 vote, the Joint Legislative Budget Committee directed state School Superintendent Tom Horne to divert $5 million from the funds given to his agency to provide state aid to public schools. The Republican-controlled panel said he should use the money instead to finance the voucher programs  programs which were not funded in the $9.9 billion budget.

In fact, House Majority Leader Tom Boone, R-Peoria, told Horne he doesn’t even need permission of the committee or the entire Legislature.

But Horne isn’t going to do that, at least not yet. He said unilaterally doing what the committee directed would be illegal  and could subject him to personal liability for misspending public money.

Horne said that, at the very least, he needs permission of the Bill Bell, director of the state Department of Administration. To that end, Horne wrote Tuesday to Gov. Janet Napolitano, Bell’s boss, asking for her OK to shift the funds.

An aide to Bell said the request is under study.

Horne, however, already is preparing for a rejection, given Napolitano’s opposition in general to vouchers. He said his next step will be to ask Attorney General Terry Goddard if the fund shift is permissible.

And if Goddard says “no,’’ Horne said he will file suit.

If Horne is successful, the money will come from the more than $3.3 billion lawmakers allocated in state aid for public schools. But legislative staffers conceded there will be extra money in that account only if the number of children who enroll in public schools this year is less than anticipated; if that is not the case, a $5 million transfer could leave the state with unfunded obligations.

Lawmakers first funded the vouchers in 2006, with $2.5 million for a program aimed at children with certain disabilities and an equal amount for children who had been in foster care.

The state Court of Appeals ruled earlier this year that the vouchers violate a constitutional provision which bars the use of state tax dollars to aid private or parochial schools.

One bit of fallout from that was that budget negotiators, looking for places to cut spending, decided not to fund the programs for the new fiscal year that began July 1.

After the budget was adopted, though, the state Supreme Court gave permission for the programs to continue while it reviewed their legality. Boone said Tuesday that gives Horne the legal go-ahead to use any money he can find.

But Horne, who is an attorney, said Boone is misreading what the high court has done.

He said the order simply permits the continued use of state funds. But Horne said the high court cannot  and did not  tell him to disregard the fact that the Legislature did not fund the programs.

The failure to fund the programs this fiscal year has led to protests from parents who said their children, who had fallen behind in public schools, were finally getting the special attention they needed. Some parents said they were trying to find the money to pay the tuition for the new school year; others are hoping for scholarships.

Napolitano has repeatedly said she does not believe public dollars should go to private and parochial schools.

But the governor agreed to these two programs in 2006 as part of a political deal to get some of her priorities. That included full funding for all-day kindergarten.