WEST WARWICK — For a district that is already looking at a potential $4-million deficit for the year that began July 1, an additional $34,131 isn’t exactly hitting the jackpot.

But it’s something.

“We’re going to take it and we’re going to apply it to our deficit,” said Michael Petrarca, the schools’ director of administration. “Every little bit helps.”

The money comes as the state begins divvying up revenues from overnight gambling at Twin River, the slot parlor in Lincoln. The General Assembly this year authorized 24-hour gambling on weekends and holidays, and stipulated that part of that additional gaming revenue would be divided among the school districts.

Every community’s share is proportional to its level of state aid, said Senate spokesman Greg Pare.

Under the initial disbursement, from overnight revenues between May 12 and June 30, West Warwick will receive $34,131.

The windfall receipts may get bigger as time goes on — but, noted Pare, “There are no guarantees, just projections.” By the state’s projections, West Warwick could receive $254,000 if gaming revenue for the rest of the year stays steady with current levels. It could get as much as $402,000 if gambling increases significantly.

But until the money hits the district’s account, officials said they aren’t counting on it.

“This School Committee is not going to anticipate 10 cents,” Chairman Daniel T. Burns Jr. said yesterday. “We’re not going to spend money we don’t have. … Any money coming in from the state will be used to pay bills. We’re not going to put it aside. We’re going to try to reduce the deficit — if we’re fortunate enough to receive the money.”

The district is still working to cut the projected deficit, said Petrarca, and will have a clearer idea of how much its budget is falling short in the months after school starts.

The School Department was allotted a $49.3-million operating budget for the current fiscal year, about $4.7 million less than it requested. Aggravating the pinch is the lack of an increase in state aid to school districts.

As part of its effort to cut costs, the district has eliminated two school buses — one for special-education students and another for general-education students — for a total savings of $112,200.

Petrarca said it hopes to save roughly $200,000 in special-education tuition now that the district has established its own programs. In recent years, the district has instituted a transitional program at Clyde Towers and an alternative day school at the West Warwick Civic Center, among other programs.

“If we didn’t have these programs, the savings in tuitions wouldn’t be there,” Petrarca said. “The money saving now is mainly derived because we’ve established those programs.”

The School Department also hopes to realize a savings by replacing departing teachers with personnel lower on the salary scale, he said.

“In October we’ll have a better idea” of the gap between spending and revenues, Petrarca said. “That’s the number we’re going

tbuford@projo.com