The impoverished city, operating under a receiver for a year, has promised $80 million worth of retirement benefits to 214 police officers and firefighters, far more than it can afford. Those workers’ pension fund will probably run out of money in October, giving Central Falls the distinction of becoming the second municipality in the United States to exhaust its pension fund, after Prichard, Ala.

“Time is running out,” warns Robert G. Flanders, the state-appointed receiver, who recently closed the public library and a community center to save money. He has no power to cancel the city’s contracts with workers, so instead he has begun approaching retired police officers and firefighters with what he describes as “the Big Ask”: will they voluntarily accept smaller benefits in the name of saving Central Falls?

Some of the retirees are in their 90s, and Central Falls, like many American cities, has not placed its police and firefighters in Social Security. Many have no other benefits to fall back on.

State lawmakers are trying to contain the damage, mindful that it would be a bad time for any state to seek help in Washington. Last month they rescinded an offer of state aid to Central Falls, just after Moody’s downgraded the city’s credit to “possibility of default.”

But the state still has risks related to the woes of its municipalities, risks that have gone largely unnoticed because it is not as big as, say, Illinois and California. Several other Rhode Island cities are sinking under big debt burdens. Even Providence, the capital, risks running out of cash in September, according to its auditor, and if it scrapes by until October, it must then come up with $60 million for its own municipal pension plan.

Some analysts fear that a Central Falls bankruptcy, and a whiff of other problems out there, could scare nervous investors away from bonds issued by Rhode Island’s other municipalities, perhaps setting off a chain reaction that could push the state itself to the brink. There is a precedent: the last American state to default on its bonds, Arkansas in 1933, got in over its head by trying to help struggling municipalities.

More recently, when local governments have veered toward bankruptcy — Orange County, Calif., in 1994; Cleveland in 1978 — neighboring municipalities have found it harder to sell their own debt. During the New York City fiscal crisis of 1975, New Jersey suddenly found its bonds harder to sell.

“That type of contagion is what you’re trying to avoid,” said James E. Spiotto, a bankruptcy specialist at the law firm Chapman Cutler, who is not involved in Rhode Island’s problems.

Rhode Island has an investment-grade credit rating, but it is in no position to bail out a string of teetering cities, or take over their shaky local pension funds the way the federal government does when some companies go bankrupt. The state treasurer, Gina M. Raimondo, says Rhode Island must first stabilize its own pension fund, which continues to require more and more cash each year, despite four overhauls since 2005 that were supposed to get the cost under control. The Securities and Exchange Commission is investigating. If the state turns out to have understated its commitments, it could deliver a new jolt to bond markets still nervous after two traumatic years.

Lawmakers in Rhode Island are trying to reassure investors. On July 1 they passed a law giving certain bonds, known as general obligations, legal priority over all other payments that municipalities must make, including retirement benefits. The measure, awaiting Gov. Lincoln Chafee’s signature, also requires Rhode Island’s cities, towns and districts to dedicate their general revenue to paying bondholders first, and to raise property taxes as much as necessary to make all payments to bondholders on time.

It gives less secure types of bonds priority, too, and makes local officials personally liable for any losses they cause by failing to comply with the new requirements.

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