Santa Clara’s fight with the 49ers over the cost of running Levi’s Stadium is about to get rougher.

A new city-ordered audit says the Niners owe Santa Clara more than $2 million for public safety and other stadium costs over the past three years — findings that the team sharply disputes.

According to a draft of the confidential 169-page audit, which we’ve obtained, the tab includes:

•$894,000 left over from a stadium construction fund that was used to cover various public safety costs during the opening year at Levi’s — but that wasn’t included in the budget approved by the city-run Stadium Authority.

•$719,000 to cover revenue that the city lost by allowing the Niners to park cars on a city-owned golf course during games and other events.

• $488,000 that the city, by its own admission, never actually billed the Niners for — largely to pay for fire crews around the stadium, and to reimburse local police for investigating the a 2014 beating of a 49ers fan inside a stadium restroom.

The report also takes aim at the Stadium Authority management, saying it lacks “controls and procedures to verify” that the city’s share of fees collected from the public and private parking lots operated by an outfit called Citypark are accurate, and saying there should be a special audit.

The Stadium Authority serves as Levi’s landlord, while the team manages the stadium day to day under a company it created called ManCo.

The outside audit, which was recommended by the Santa Clara County civil grand jury looking to the management of the stadium, is the latest fodder in the city’s war with the Niners over how the stadium is being run.

The Niners declined to discuss the findings in detail, saying the city had given them until this coming Friday to respond.

However, the team did push back on the audit finding that $894,000 from the construction fund had been used improperly to pay for public safety.

As the Niners tell it, the city’s own stadium representative elected to use the surplus funds for public safety “preplanning” to avoid tapping into Santa Clara’s general fund.

“These costs were paid at the request of the Stadium Authority’s finance director in accordance with construction fund practices,” said 49ers spokesman Bob Lange.

He also said the Niners are required to pay a set figure (currently $1.9 million a year) for public safety — with the city owing anything over that amount.

“We have paid every single bill we have received from the city of Santa Clara,” Lange said.

Santa Clara Mayor Lisa Gillmor said the Niners’ version of how the construction money was to be used “makes me laugh” — but she also declined to discuss the audit until it’s officially released.

However, Gillmor did say that whatever the final numbers are, auditors had already found that some spending on the stadium — most notably, the money the city has fronted for police and fire services, but hasn’t billed the team for — violated a voter-passed initiative barring the city’s general fund from being used to operate the stadium.

Gillmor is part of the City Council’s new, self-described “Soccer Mom” majority — which is still unhappy that the team tried to take control of youth soccer fields for Levi’s parking. The Soccer Moms have accused the 49ers of withholding documents that could reveal whether the city is improperly spending even more money than the audit has found.

Gillmor, meanwhile, is pushing for the hiring of a new Stadium Authority manager to better look after the city’s financial interests.

Fire alarm: In the aftermath of the Ghost Ship fire that claimed 36 lives, Oakland Mayor Libby Schaaf called for a top-down review of the Fire Department’s understaffed inspection bureau and a better computer system for keeping track of buildings that need checking.

After six months and a second deadly fire that the mayor said “further underscores the urgent need for reforms,” not that much has changed.

Inspection issues played a big role in both the Dec. 2 fire at the converted Ghost Ship warehouse, which had long escaped the city’s scrutiny, and a March 27 fire at a halfway house on San Pablo Avenue that killed four people. Firefighters had flagged problems there, but inspectors were slow to order changes.

The city is “in the process” of hiring seven inspectors, Hunt said, but there is no set date for when they will actually hit the streets.

It’s pretty much the same story on finding a fire chief to replace Teresa Deloach Reed, who was the target of criticism for the inspection deficiencies, went on leave and then retired in March. Hunt said the city has conducted a series of “community input meetings” to “guide the recruiter toward the types of candidates” who would make a good chief. The goal is to have a chief by June or July.

Also in the works: a new computer system aimed at keeping buildings like the Ghost Ship from falling through the cracks. It’s moving toward City Council approval, but there’s no estimate for when it might come online.

In other words, six months after the promised fire inspection reforms, they are all very much a work in progress.

San Francisco Chronicle columnists Phillip Matier and Andrew Ross appear Sundays, Mondays and Wednesdays. Matier can be seen on the KPIX TV morning and evening news. He can also be heard on KCBS radio Monday through Friday at 7:50 a.m. and 5:50 p.m. Got a tip? Call (415) 777-8815, or email matierandross@sfchronicle.com. Twitter: @matierandross