DOVER — The state House on Thursday overwhelmingly passed a bill allowing public school students to opt out of state standardized testing, but the legislation faces a possible veto by Gov. Jack Markell if it passes the Senate.

The bill, which was the subject of a contentious committee hearing last month, cleared the House on a 36-to-3 vote with virtually no debate.

“This is simply a parental rights bill,” said chief sponsor Rep. John Kowalko, D-Newark, adding that the legislation was not a reflection on the Markell administration or the state Department of Education.

House Education Committee chairman Earl Jaques, who butted heads with Kowalko in last month’s committee hearing, said the bill was not needed because parents have already been choosing for their children to skip the state test, and that local districts can handle the issue.

“They don’t need any interference from DOE or anybody else,” said Jaques, D-Glasgow.

Republican Minority Leader Danny Short said after the bipartisan vote that there needs to be a serious conversation about public education in Delaware.

“This system, in my opinion, is broken,” said Short, R-Seaford.

Markell, in a telephone interview from Switzerland, disagreed.

“I don’t think it’s a good bill,” Markell said, who touted recent improvements in state schools, including higher graduation rates, lower dropout rates and more students taking and passing advanced placement tests.

The legislation allows parents and guardians to have their children skip the annual state assessment without any academic or disciplinary repercussions for the students. The legislation takes aim specifically at the Smarter Balanced Assessment, a new test that is tied to Common Core education standards being adopted in Delaware and many other states. Markell was an early proponent of Common Core.

Administration officials pointed out that the state could face a loss of federal funding if test participation drops below required levels.

Markell also noted that members of the civil rights community in Delaware and other states have supported annual assessments as an effective way to identify and address the needs of minority students.

At the same time, administration officials have been sympathetic to concerns that students may be subjected to too much testing.

Markell in March announced a review of tests administered by the state, local school districts, and individual schools aimed at decreasing the testing burden on students and teachers and increasing time available for teaching.