ALBANY — The good news is New York State, in a summertime gift from Washington, is poised to suddenly get $607 million in federal dollars to pump into its 700 school districts.

The bad news? No one knows how much any district will get, or all the restrictions on how the money can be spent, or what happens when the new aid dries up. And no one is quite sure whether state lawmakers must quickly return to the Capitol to approve how the money is steered, or whether Gov. David A. Paterson can unilaterally decide.

All this confusion comes with the fall semester just around the corner. Districts already have set their classroom assignments, made decisions about staffing levels and finalized their budgets for the year.

That leaves many districts wondering if they even have the time or legal authority to spend the newfound money, let alone the logistical ability to rehire laid-off teachers or start new classroom programs before classes begin next month.

“That having been said, we’re not complaining. We’ll work through these issues,” said Timothy Kremer, executive director of the New York State School Boards Association.

Everyone thought state financial discussions were over with passage of the state budget, but Congress last week gave final passage to a $10 billion Education Jobs Fund, of which New York is in line to get $607 million.

State officials were thrilled to get the extra money from Washington, even after education funding was cut $1.4 billion to help balance New York’s budget. But, as often is the case with budgeting in Albany, unexpected new money can sometimes produce more fights than consensus.

And confusion. For instance, U. S. Sen. Charles E. Schumer released—with the help of the state’s largest teachers union — a district-by-district accounting of how much money they would get from the new federal aid package. But officials in Albany say Schumer’s numbers were premature and not based on any negotiations in Albany about which formula to use to spread the money around. Those formulas can widely vary in terms of winners and losers.

That all leaves uncertain, for example, if Buffalo’s school district will get the $8 million Schumer touted.

At first, the new funding was lauded as saving districts in New York from going through with thousands of teacher layoffs. That story has changed a bit. Now, the funding can go to restore not just laid-off teachers, but to pay for salaries of those already on the payroll, or to even add new jobs. And it’s not just teacher positions that can be funded, but a range of posts — from librarians and nurses to janitors and occupational therapists.

Some schools are talking about using the money to help pay for extra help to deal with the state’s decision to raise the bar on elementary school testing, a move that recently saw math and English proficiency scores drop sharply.

The new money can’t go to district administration jobs. Nor can it go into rainy day accounts or to pay off debt. It also can’t go to lower this year’s property tax bills, as some state lawmakers facing voters this fall envisioned.

Federal officials also are signaling that not all the money has to be spent in the upcoming school year. That gives wide latitude to districts that already have their budgets and staffing levels set for this school year.

Assistant U. S. Education Secretary Carmel Martin told reporters last week after the bill was signed by President Obama that districts are “encouraged” to spend all the money they get this year, but added they technically have until September 2012.

“Quite a number of districts felt they already made the tough decisions and some have gone so far as to tell students who their teachers are going to be,” said Robert Lowry, deputy director of the New York State Council of School Superintendents. “But we’re concerned for next year, and apparently this money could be used to put together better budgets a year from now.”

The funding’s timing is causing other logistical issues, and potential real problems down the road. Besides already having adopted their budgets and set staffing levels, districts are now in the final weeks of a statewide early retirement program intended to reduce the ranks of older, higher-paid employees. How this new federal money affects that — and if some districts might rescind some of those early retirements — is not known.

Then there are future issues. What, for instance, if a school uses the money to start some new classroom or after-school teaching program? What happens to that program if all the money is spent this year? Will local taxpayers be asked next year to pay for it, or will it just disappear?

Critics have said the new money for schools only encourages them to maintain higher-than-needed staffing levels, and that the drop in spending increases for some districts this year was necessary rightsizing. Now, this only delays the pain another year, they warn.

The State Senate is floating the idea of coming back to Albany in two weeks. The Assembly has been reluctant for a number of reasons. The governor, meanwhile, has until Sept. 9 to return a brief application — sent to the states Friday — for New York’s money share.

“Our understanding is the Legislature, obviously, has to approve the legislation and funding mechanism. The governor is working on a proposal . . .,” said Erik Kriss, a Paterson budget division spokesman.

There are questions whether districts could spend any of the money without Albany’s approval. That is because their spending levels were already set — most during May’s statewide school budget votes — and they cannot exceed those levels on their own.

On the brief application form from the U. S. Education Department, Paterson is given two choices on how to divvy up the money for kindergarten through 12th grades: a federal formula or one used by the state. If the federal formula is used, poorer districts, like Buffalo, would do better; New York City would get 70 percent of the funds under that scenario. A state formula, which includes some political calculations, would spread the money around more evenly across the state.

Officials for the Senate and Assembly said a spending plan is still being negotiated with the governor.

If the money is to be spent this year, schools need answers.

“The more information districts have the sooner the better,” said Lowry of the superintendents group.

Education Secretary Arne Duncan told reporters in a conference call the money is coming soon. He also cautioned states not to try to dip into the money to deal with their own budget issues.