FLEMINGTON, New Jersey — Rep. Andy Kim won his third straight county convention on Sunday, beating his top rival, first lady Tammy Murphy, in his bid for the Democratic nomination for the Senate.

But Kim’s victory came after the Hunterdon County convention was briefly thrown into disarray when the county chair — a Murphy ally — proposed changing the endorsement rules. It would have allowed candidates with 30 percent of the vote to share the so-called county line, the valuable primary ballot positioning that party-endorsed candidates receive.

The proposal was met with cursing and screams from the convention delegates and beaten down in a hand vote. But if the rule change went through, it would have meant that Kim would have had to share the line with Murphy in the county — likely putting them on equal footing, visually, with primary voters.

Kim’s victory here means he wins the county line, placing him in the same ballot column as other party-endorsed candidates — a unique and hugely important feature of New Jersey’s primary system. Each county party in the state differs in how the line is awarded — some have conventions where local Democrats like precinct leaders vote on who they want to support. In other large Democratic strongholds, the support of a local party boss is enough to get the valuable ballot positioning — in those parts of the state, Murphy enjoys a strong advantage over Kim.

Kim won the Hunterdon contest 120 votes to Murphy’s 64, or 62 percent to 33 percent. He and Murphy are the frontrunners in the race to replace indicted Sen. Bob Menendez, who has not said whether he is seeking reelection.

Hunterdon County is New Jersey’s fourth smallest county by population, and Democrats have not held a single countywide elected office here since 1982. But it is the third consecutive Democratic county convention win for Kim. And unlike the state’s first two Democratic conventions in Burlington and Monmouth, both of which Kim won handily, Hunterdon has a unique qualifier: It is the first county that neither Kim nor Murphy have any natural political roots. In that way, Hunterdon may offer a preview at how Democratic voters who don’t have a clear connection to Kim or Murphy may react to their candidacies.

Kim represents most of Burlington County, where he grew up, and around a third of Monmouth County. Murphy has lived in Monmouth County for well over two decades.

When asked if Kim had momentum in the race, Murphy said: “No, he does not. … he oversees 35 percent of Monmouth County [in Congress], that makes sense. Burlington, that’s his county.” She declined to address Hunterdon.

Hunterdon Democratic County Chair Arlene Quiñones Perez told convention delegates that she wanted to make the balloting changes Sunday because of a letter sent by Kim and two other Senate candidates, Patricia Campos-Medina and Lawrence Hamm, calling for an “office block” primary setup in all 19 of New Jersey’s 21 counties that do not currently use it.

Kim, however, was not in favor of the change on Sunday. And surrendering the line in Hunterdon County would have put him at a statewide disadvantage since Murphy would presumably still have the prominent ballot positioning in other key Democratic strongholds in the state where she has support.

Murphy told reporters that she was unaware of the convention proposal until Perez announced it from the convention floor.

“I thought it actually might have made sense, but I had no vote in it,” Murphy told reporters. She did not directly answer whether she would support a similar measure in counties that she is expected to win, such as Middlesex.

“I’m not going to dictate how different county parties function — I think that’s not right. But again, if there are good ideas … then I’m all in,” she said.

Kim also heavily criticized the manner by which the rule change was proposed by county leaders.

“They decided that it’s good to have something sprung upon a convention at the last possible second without any ability to discuss or deliberate,” Kim said. “You saw the reaction from people. They don’t like that.”

He added that, though he would have supported a shared line system had it been in place in all 19 counties, “I made it very clear what I want, which is every single county to be able to do the office block.”

Hunterdon County does not represent a large prize in the broader Democratic primary contest: There are just over 30,000 registered Democrats here, representing 1.2 percent of all Democrats in the state. By comparison, Burlington and Monmouth counties each represent about 5.6 percent of all Democrats in the state.

Sue Altman, who is running unopposed for the Democratic ticket in New Jersey’s 7th Congressional District, also received the county endorsement unanimously by voice vote. She is running to unseat Rep. Tom Kean, Jr., who flipped the district red in 2022 in a narrow win over Democrat Tom Malinowski. The race is considered among the most competitive in 2024.