In early 2013, barely a month after she was sworn into office, City Councilwoman LaToya Cantrell issued a statement forcefully proclaiming her opposition to the demolition of a century-old house at 820 Gen. Pershing St. that she said was essential to “the residential fabric of the community.”

On Thursday — citing an impasse that fellow Councilwoman Stacy Head described as more of a “hostage” situation — Cantrell voted to approve the demolition of the same property.

She declined to explain the reason for her change of heart, but residents who met with her said she told them her decision stemmed from concerns about the viability of the city’s overall process for denying the demolition of historic properties.

Created in 2008, the Neighborhood Conservation District Committee governs the demolition of buildings in historic areas that fall outside the city’s officially designated historic districts. The NCDC is made up of 13 members — one appointed by each of the seven council members, one appointed by the mayor and five representatives from city departments such as Safety and Permits and the City Planning Commission.

Anyone attempting to tear down a building within the NCDC’s jurisdiction must make their case before that panel first. If they are rejected there, they can appeal to the City Council.

The owners of the house at 820 Gen. Pershing have participated in that process twice in recent years, with the NCDC first denying them permission to demolish in late 2012. Cantrell was elected to the City Council that December; in January, she issued a statement announcing her opposition to the demolition, citing that stance on her campaign website as evidence of her support for historic preservation.

A new owner of the house returned to the NCDC for another try in June of this year. This time, the NCDC, which has several vacant seats, voted 5-2 to reject the demolition. The owners appealed that decision to the council, and the request was pending for several weeks as the Sept. 9 deadline for a decision drew nearer.

On Wednesday, a day before the final City Council meeting before the deadline, Cantrell invited neighbors to her office for what turned into a six-hour meeting to discuss her decision to allow the demolition. She refused to let a reporter attend that meeting and, in a brief interview afterward, declined to explain her support for a demolition she once so ardently opposed.

But several residents who attended the meeting said Cantrell told them her change of heart stemmed from ongoing questions about the validity of the NCDC process.

“She says the NCDC process is not legal,” said Faye Lieder, a neighbor who has spearheaded efforts to preserve the Gen. Pershing property.

The concern among city officials, according to the residents’ account, is that a flaw in the structure of the NCDC leaves decisions made by the panel so open to legal challenge that they cannot be successfully defended in court.

“Right now, anybody can demolish anything,” Lieder said.

Cantrell told the residents she could not support a decision that leaves the city open to a lawsuit, the neighbors said.

The scope of the problem with the NCDC — how many demolition denials may be ripe for legal challenge and how long city officials have known about it — is unclear, as officials involved largely refused to discuss it last week.

Cantrell declined to discuss the neighbors’ account of the meeting. A representative of the Preservation Resource Center who attended it also refused comment. And Garnesha Crawford, a spokeswoman for Mayor Mitch Landrieu, said only, “We don’t have a comment today,” in response to questions about the NCDC’s legal vulnerability.

When the demolition request for 820 Gen. Pershing reached the council on Thursday, officials were likewise circumspect in their explanation of why it could not simply be denied, as it was before.

Cantrell said the request was at an “impasse” and gave two reasons for her support for the demolition. First, she said, the owner had signed an agreement to keep the lot as a garden, rather than a parking lot or another commercial use, and, second, the building would continue to deteriorate if the demolition was denied — the latter rationale essentially condoning a policy of demolition by neglect, usually condemned by preservationists.

Only Head, who represented the neighborhood before being elected to her at-large council seat, challenged the demolition, which ultimately passed 6-1.

“I think we’re being held hostage by some people who aren’t doing what they should have done,” Head said.

In an interview outside the City Council meeting, Head said it was “absurd” to allow a demolition because of potential challenges to the panel.

“There have been legal challenges to the NCDC. Developers don’t like being told ‘no,’ ” she said. “But if we stopped enforcing the rules because of challenges, I’m not sure we’d need a government. There are very few laws that are already enforced that haven’t been challenged in court.”

But at the same time, Head is working with the city administration to craft an overhaul of the NCDC. A draft of a new ordinance would rename it the Neighborhood Conservation District Advisory Committee and limit its function to “counsel and advice.” All of the city officials on the panel would be removed, leaving only seven members appointed by the council.

The goal of the legislation, Head said, is to place the board squarely under the legislative branch instead of the executive branch and thus “remove an argument” that developers use in court against demolition denials. The existing process is sound, she said, but her ordinance will strengthen it.

As of Wednesday night, the new ordinance still was slated to be introduced at the next day’s City Council meeting and even was mentioned in a council news release about agenda items scheduled to be heard. But on Thursday the council clerk said it had been deferred to the council’s Sept. 18 meeting.

No matter when the council takes up the proposal, and regardless of how many other demolition denials could be in peril, one thing is clear: It is likely too late to save the house on Gen. Pershing. Neighbors have said the owner plans to begin demolition within a week.

“We fell through the cracks,” Lieder said.