The New Hampshire Senate split from the House Thursday when it scuttled a controversial bill that would allow students to enroll in any public school in the state.

Although the bill could still pass this year through the state budget process, the Senate’s vote signaled that the Republican-controlled legislature is divided on how to proceed with the closely-watched proposal. The House voted to approve it in March and included it in the budget bill that representatives approved last month.

The open enrollment law would bring New Hampshire in line with about one-third of states nationally, where parents are allowed to send their students to districts outside of the one where they live. Currently, individual school districts control whether New Hampshire students can enroll elsewhere on their home district’s dime.

The proposal has been championed by school choice advocates, who argue it would increase competition and allow students who live in low-performing districts to seek better-performing schools elsewhere. In contrast, opponents have contended it would exacerbate inequalities in education, causing low-performing sending districts to lose students and money.

Following the Senate’s vote, which it made without discussion, Sen. Ruth Ward, the chair of the Senate Education Committee, expressed support for the general concept of open enrollment but said the legislature needed more time to iron out the details.

“It is a new concept, and a new concept always brings questions and concerns,” Ward said. “So I think we have to look at it.”

Ward said she was most concerned about the cost-sharing formula. Under the current language in the bill, HB 741, the school district in which the student resides would be responsible for paying 80% of its own average cost per pupil.

That could become complicated, Ward indicated, if the average cost per pupil differed markedly between the sending and receiving districts, in essence allowing students to receive a superior education at a discounted price.

Rep. Glenn Cordelli, the bill’s prime sponsor and the chair of the House Education Policy and Administration Committee, did not respond to a request for comment on the Senate’s vote.

The bill will have a final chance to pass the Senate when it takes up the state budget in the coming weeks.