A push to tax multimillion-dollar second homes in New York City has been billed by Gov. Kathy Hochul and Mayor Zohran Mamdani as a civic mandate for the ultrawealthy to contribute more to society.

But as leaders in the State Capitol seek to incorporate the tax proposal into the state budget, the lofty rhetoric has been undermined by confusing information flowing from Ms. Hochul’s office about how such a tax would work.

The problems start with the numbers and the math.

To raise $500 million for the city, Ms. Hochul initially said the so-called pied-à-terre tax would apply to 13,000 homes, a number that her staff pulled from a 2023 report by the city comptroller. Now, aides to Ms. Hochul are saying that the 13,000 figure was an early estimate requiring more analysis and was subject to change.

The governor’s team had first said the tax would be based on second homes with an assessed value of $5 million or more. But there is very little correlation between a property’s assessed value — a specific and complex measure calculated as part of the property valuation process — and actual market value.

The city does not use sales comparisons or recent listings to value condos and co-ops. Under a state law passed in the 1980s, the city is required to compare the units to rentals of similar size and age, assessed on the potential income that rental might bring in. There are not great rental comparisons for the highest-end condos and co-ops, dragging down their assessments; in some cases, these condo buildings are even compared to rental buildings with rent-regulated units.

An analysis of city records conducted by Marketproof, a real estate data analysis firm, found just three residential properties in New York City with assessed values of $5 million or more.

One of the three was the notoriously expensive penthouse bought in 2019 by the billionaire financier Kenneth Griffin for $238 million.Its assessed value, according to city records, is just under $7 million. Another condo, on the 57th floor of another Midtown luxury building, sold in December for more than $21 million, but it has an assessed value of around $1.3 million.

Jennifer Goodman, a spokeswoman for the governor, declined to offer specifics about the pied-à-terre tax proposal, saying this week that they were still being negotiated. The governor’s office said that they had wrongly described at first how the tax might work, and it is not going to be based solely on the assessed value of properties.

Instead, Ms. Goodman said, apartments subject to the tax would be determined by “a model that captures properties worth over $5 million through the use of various mechanisms such as comparable sales data where applicable.”

That raises another set of problems, as there is no official and consistent measure of how much properties in New York City may actually be worth on the market.

Building that kind of information is possible, but has not typically been done before by the city, said Kael Goodman, the president and chief executive of Marketproof.

“To get from doable on a technical basis, to doable on a practical basis — those two things are not the same,” Mr. Goodman said.

To demonstrate how such a tax could work, Marketproof created its own model analyzing more than 1.14 million tax parcels. Since there’s currently no official way to tell if a particular unit is a pied-à-terre, the company used a proxy: the subset of properties where the property tax bill was sent to a different address, indicating the owner didn’t live in the unit.

Then it looked at transactions recorded in city property records to find the units with market values over $5 million.

Marketproof estimates about 6,380 properties would be affected.

That analysis shows that certain well-known features of the city skyline, many clustered around Central Park — Central Park Tower, 432 Park Avenue, One57, 220 Central Park South, 15 Central Park West — would be potentially subject to the tax surcharge, representing huge sources of revenue for the city. The 280 units in just those five buildings might owe more than $100 million in taxes annually.

Still, it may be challenging to make this all work. Unlike many suburban cities and neighborhoods, where it is relatively easy to find the market value of single-family homes based on comparable sales on any given street, it’s difficult to compare values across condos and co-ops.

“That would be crossing a gap not previously crossed,” Mr. Goodman said. “That would be opening up a conversation among property owners that previous government officials have been unable to have a successful conversation about. They’ve just been unsuccessful in doing it because it’s way too complicated.”

It’s not clear whether the state or the city would have the capacity to come up with these valuations every year, and how public officials would deal with the expected legal challenges to any valuations.

A report about the tax released on Thursday by the New York City comptroller, Mark Levine, found that the city Finance Department would most likely have to audit property owners’ claims about who lives or doesn’t live in any apartment. The report noted that “lapses” in the auditing capacity and accuracy “would reduce revenues and multiply taxpayers’ appeals and lawsuits.”

The report also said that it might be difficult to categorize condos and co-ops that were owned by out-of-towners but were being rented out to city residents, or units that were owned by limited liability companies or trusts, among other potential pitfalls.

“Each of these decisions can shift collections by tens of millions of dollars,” the report said.

So far, those details remain murky, even with senior city administration officials meet daily with state leaders, according to City Hall.

A senior aide to the governor said that state officials were not overly concerned about the complexities of determining market values. Negotiations were continuing over how much of the specific methodology would be written into the legislation, or decided later by the city.

A bigger concern, the aide said, was how officials would determine whether any given property was being used as a second home.

The negotiations come as Mr. Mamdani and other elected officials clamor for Ms. Hochul to increase taxes to fund an expanded safety net and help the city close a multibillion-dollar deficit. A coalition of powerful unions, including several that endorsed the governor’s re-election campaign, has also signed on, sending a letter last week to her and legislative leaders pleading for tax hikes on the wealthy.

On Tuesday, Mr. Mamdani and his sometimes political adversary, Council Speaker Julie Menin, said they would delay announcing an update to the city budget so they could jointly push for the state to reduce a tax credit that primarily benefits wealthy business owners, which they said could end up raising a billion dollars in revenue for the city.

Both this plan and the second-home tax proposal would need to be included in the state budget, which is still be negotiated and is now a month overdue. Ms. Hochul remains committed to the tax on second homes, but appeared unlikely to support other new taxes.

“Hochul is running out of excuses to not tax the rich in her final budget,” said Grace Mausser, a co-chair of the New York chapter of the Democratic Socialists of America.

The D.S.A. is a close ally of Mr. Mamdani, who is a member, and both have aggressively called on the city’s wealthiest businesses and residents to shoulder a heavier burden. They have even named specific billionaires like Mr. Griffin, who they say are a drain on the city and its finances.

Mr. Griffin, who has spent close to $95 million on real estate purchases in the city since the beginning of 2025, pushed back on these assertions, saying his companies and activity creates tens of thousands of jobs for the city.

“You can win political points by making an example of Ken Griffin, and they seem to have done that. Kudos to them for winning some political points,” Mr. Goodman said. “But achieving the tax goals is a different thing.”