Last year, the state paid almost $77 million in overtime to government employees, an amount that would go a long way toward plugging perennial holes in the state’s budget. So, what if the state just stopped paying overtime? Could that solve the state’s fiscal woes?

The short answer is no, according to state and union officials, who agree that overtime is unavoidable in certain government programs. Those include the so-called 24/7 operations, in which positions have to be staffed around the clock and absent workers must be replaced with someone else. Those include the state prison, state police patrols and the hospital and group home programs of the Department of Mental Health, Retardation and Hospitals.

But where the state and the unions disagree is whether work rules contained in union contracts are unnecessarily forcing the state to rack up overtime.

“Some of this stuff is really, really very costly, very onerous,” said Beverly E. Najarian, director of the state Department of Administration. “When I first came here, all of these rules seemed so foreign to me. If you would look at other unions in the private sector, you would not find these things. They are all detrimental to the efficiency and management of any operation.”

But union leaders say the biggest factor driving up overtime costs is the state’s refusal to hire an appropriate number of workers.

“There’s too many vacant positions,” said Dennis R. Grilli, executive director of Rhode Island Council 94, American Federation of State, County and Municipal Employees. “I know what their philosophy is: to do more with less. It’s just not working.”

Council 94 represents 5,000 state employees, about a third of the state’s work force. The union’s largest presence is in Mental Health, Retardation and Hospitals, which paid about $20.6 million in overtime last year, according to the state controller’s office. That represents about 27 percent of the total overtime and was second only to the Department of Corrections among 24 departments.

How much do state officials figure contract work rules cost the state in overtime?

“It’s really difficult to ascertain what is created in terms of overtime,” Najarian said. She was pressed to come up with an approximate proportion of the $77 million. Her best estimate was, “a lot.”

Najarian gave several examples from 39 separate union contracts that she said hamper the administration’s ability to manage overtime and other costs more effectively.

A prime case she cited was limitations on who can fill absences. At MHRH’s Eleanor Slater Hospital, two separate unions represent nurses. “The duties and whatever are exactly the same,” Najarian said.

But, if a nurse from one union is absent in any given shift, hospital administrators cannot fill the vacancy with a nurse from the other union who is already scheduled to work the same shift. Instead, they must pay overtime, either to call in a nurse from the first union or keep one on to work a second shift that day.

Similar restrictions prevent administrators from temporarily moving workers from one motor vehicle registry office to another or from having workers in the registry’s titles-processing department help out at customer-service windows during an unexpected rush.

But Grilli cited a recent change agreed to by his union that helped eliminate a similar problem at MHRH, where housekeepers at various facilities were in different bargaining units. The union agreed to management’s request to consolidate those units, he said. “We’re willing to talk to them.”

Richard Ferruccio, president of the union that represents correctional officers at the Adult Correctional Institutions, the largest user of overtime dollars, echoed Grilli’s comments. “If there’s a common sense rule change, the process to do it is through contract negotiations,” he said. He said his union has suggested budget-cutting changes. “There are a number of areas the state could save money on, but the state chooses not to hear what we have to say.”

Ferruccio’s union, the Rhode Island Brotherhood of Correctional Officers, is in contract arbitration with the state, and declined to comment on specifics, citing a directive from the arbitrator. Administrators at the prison similarly declined to comment for this story.

But last month, Corrections director Ashbel T. Wall II listed contract prohibitions against moving “surplus” guards from one facility to another as a force driving up overtime costs. “We don’t have maximum flexibility to deploy our staff to fill vacancies,” Wall said at the time.

In the past, the union has disputed whether the prison has had enough “surplus” correctional officers to move them between facilities.

Wall also has said that overtime is the preferred way of covering for absences. “It’s more cost-effective to use overtime to plug those gaps when an officer can’t be on-post than to hire additional staff.”

But Ferruccio said last month that Wall has pushed it too far. “There’s an extreme shortage of correctional officers,” he said. “When we are so short-staffed, like we have been the last few years, there’s a lot of overtime.”

One reason state administrators find overtime more attractive than hiring additional workers is the benefits package that state workers receive.

“We have absolutely one of the richest benefit plans around,” Najarian said.

Grilli countered, “I think we’re getting a fair wage and benefit package. I don’t think it’s excessive.”

Najarian described how the employees’ shares for health insurance are calculated. For most Rhode Island state workers, it is based on a percentage of the worker’s pay. In other states, including Massachusetts, workers pay a percentage of the insurance premium.

That makes a difference because, as health-care premiums escalate, the State of Rhode Island picks up a larger share of the cost.

Najarian also said that Rhode Island state workers pay less than their counterparts in Massachusetts — or in private industry.

She said the premium for a family health-care package is $16,148. Most Rhode Island state workers contribute 2.5 percent of their pay. With an average state worker having a salary of $46,600, the employee’s share would be about $1,165.

But a survey Najarian cited showed Massachusetts workers contributing 25 percent of the premium. The same formula applied in Rhode Island would result in employees paying $4,037 each.

When multiplied by roughly 15,000 full-time workers, the difference between the two formulas would be $43 million.

AT MHRH, Director Ellen R. Nelson said overtime related to direct care of patients is unavoidable, because someone needs to fill shifts during absences. But, she added, she has instituted controls on non-direct-care overtime — including that it must be approved by her. “There’s just zero overtime.”

One exception was the recent emergency when buildings at MHRH’s facilities in Cranston lost electricity. Workers not only put in extra time, but pitched in where needed, without regard to limitations in contracts.

Nelson praised her workers for their flexibility during the emergency, and said she hopes that other problems — including areas of the contract she finds limiting — can be worked out cooperatively. “We’re in a quagmire here. The only way you get out of a quagmire is work together.”

One area that she hopes to address is a contract provision for union business. Union officials who also work for the state can be scheduled for weeks off, with pay, to handle union-related duties, such as meeting with other workers. But those union officials can also put in for extra shifts that week and be paid overtime, at the same time the state may be paying someone else overtime to cover the union official’s regular shift.

Nelson did not offer a solution, saying she wants to hear suggestions from the unions.

pparker@projo.com