CRANSTON –– With school officials predicting they will run out of money before the fiscal year ends, in June, it seems increasingly likely that they will sue the city for $4.4 million in the coming weeks in what is known as a “Caruolo action.”

With the specter of a lawsuit hanging over City Hall, a pressing question has emerged in recent days: where will the cash-strapped municipality find the money to pay the schools if it loses?

None of the answers is all that appetizing –– or, in some cases, even practical.

With only two months left in the fiscal year, layoffs or furloughs would probably not free up the amount of money the schools are seeking, city officials acknowledge.

Administration officials have talked of selling three city-owned buildings to plug the budget hole, but now say they will sell just one, if that, by the end of the fiscal year.

And a supplemental property tax increase is anathema to a mayor and City Council facing re-election this fall.

That leaves one viable option, it would seem: tapping the city’s cash reserve, which is a touchy subject in a city only a few years removed from financial meltdown and junk-bond status under former Mayor John O’Leary.

Republican critics of Mayor Michael T. Napolitano, a Democrat, have already criticized him for plans to mine the reserve to the tune of $2.7 million for next year’s city budget.

And they are sure to pile on if he elects to tap the so-called “rainy day fund” even earlier to pay a Caruolo judgment or pretrial settlement.

But administration officials, who predict the reserve will reach about $20 million by the end of the fiscal year, say the fund is made for tight times like these.

“The reason you build a reserve is for the tough days –– the rainy days,” said Corsino Delgado, the mayor’s finance director.

A chief concern, when tapping the reserve, is how it will affect the city’s bond rating, which influences the cost of borrowing.

Former Mayor Stephen P. Laffey, a Republican who succeeded O’Leary, a Democrat, began to repair the city’s battered rating.

Napolitano continued to build on that rating during his first year in office.

Delgado said he was confident the city’s now-middling bond rating would hold up if the city had to dip into the reserves to pay out a Caruolo judgment.

School officials said they are aware of the political difficulties surrounding the rainy-day fund.

“It’s a very sensitive issue –– and by the way, rightfully so,” said Michael A. Traficante, the chairman of the School Committee.

Nonetheless, Traficante said, the schools will push the administration and City Council to tap the reserve in the coming days.

If they decline to settle, he said, the schools “will have very little choice but to go Caruolo” and, if victorious, force the move.

The district has been threatening a Caruolo lawsuit for months, arguing that it never got enough money from the city and state for the current fiscal year.

If the school district were to prevail and win millions of dollars, city officials say they would have to add a similar amount to the schools’ budget next year to comply with a state law that forbids any reduction in education funding from year to year.

Timothy C. Duffy, executive director of the Rhode Island Association of School Committees, said the city would not actually be required to pony up the money again under the Caruolo law.

But practically speaking, he said, the city might be wise to put up the cash since it would be open to another Caruolo lawsuit next year.

Either way, the city would have to come up with millions.

Continuing to dip into the reserve would be unsustainable, city officials said, raising the prospect of cuts on the municipal side of the budget or a property tax increase.

Napolitano has avoided proposing a tax hike to date and seems unlikely to bend in an election year.

But his director of administration, Ernest J. Carlucci, said yesterday that he could not take any options off the table.

dscharfe@projo.com