New York has battled for years for more money from the federal government to combat terrorism, but questions are now arising about how that money is being spent.

While state and local leaders have shown a mostly united front in their efforts to get more of the terrorism dollars doled out by the Department of Homeland Security, back home, divisions have grown over who gets the money, and for what.

Some officials complain that the state is shaving off millions of the city’s grant money from the Urban Area Security Initiative for unknown purposes, while a recent federal audit found “questionable expenditures” by city agencies and a flawed accountability system.

For the past few years, the state has taken 20% of the city’s local terrorism-fighting grant under UASI — tens of millions of dollars the state can spend on its own projects. Although under law, the state is allowed to take the money, some officials, including the New York City Police Department, say they believe local agencies could put the money to better use.

“We’d like to see all of terrorism grants go 100% to the locality — on a threat-based formula with no pass-through to the state,” a spokesman for the police department, Deputy Commissioner Paul Browne, said.

Council Member Peter Vallone Jr., who chairs the Public Safety Committee, called the state’s 20% take “outrageous.”

He said he has pressed the New York State Office of Homeland Security, which administers the grants, to publicize what programs are getting its portion of the money, to no avail.

Nor has the state conferred with the police department, Commissioner Raymond Kelly said.

“We don’t know how they’re spending that money, quite frankly,” he told the City Council at a hearing this week.

A spokesman for Mayor Bloomberg, Jason Post, said the mayor believed the state money should be allocated based on risk, noting that the city was the most high-risk area in the state. But he also acknowledged that some areas outside the city may also be at risk.

The city’s share of the UASI grant last year was nearly $78 million, the bulk of which went to the police department. The numbers have fluctuated: In 2003, the only year the federal government gave the money directly to the city, the share was $25 million, while it was $89 million in 2005.

According to one state official, a working group including representatives from New York City advises the state on how to administer its share. The state Department of Homeland Security did not respond to repeated questions this week about its share of the funds or the makeup of the working group, saying it had not been authorized to do so by the governor’s office.

A senior fellow at the Heritage Foundation who studies counterterrorism, James Carafano, said the amount New York State takes from the city is “unbelievable,” but he said it is just one of myriad problems with the grant program.

“We don’t have any transparency,” he said. “It’s kind of like checkbooks gone wild.”

In the federal audit, published in March by the Office of the Inspector General, inspectors cited problems such as spending on a city student health record system that was supposed to detect bioterrorism. The city employees who use the system told auditors that in reality, the system had “no bioterrorism application.”

The audit also found that the city had an antiquated paper-based method of keeping track of its spending and suggested that the federal government follow up on whether the city was purchasing the equipment authorized by the grant.

Mr. Post said the city was working to improve its inventory tracking, but noted that the audit was of state and federal oversight practices, not the city’s spending.

“The audit was of them,” he said.