As New York State grapples with an increasing number of suspected child-abuse-related deaths, the unions representing Nassau and Suffolk’s child protective workers have been rallying support for a measure that would cap the number of child abuse investigations handled by each worker.

The heads of Nassau’s Civil Service Employees Association and the Suffolk County Association of Municipal Employees are urging Gov. Andrew M. Cuomo to sign a bill approved by the State Legislature last month that establishes a caseload of 15 per month. They say caseworkers, who often put themselves at risk dealing with hostile parents, have been overwhelmed with caseloads that sometimes exceed 20 per month.

Union leaders and the state sponsors of the measure say the cap will give child abuse investigators adequate time to probe claims. They cite a 2006 state study that recommended a limit of 12 cases per worker and state data that show a spike in the number of child-abuse-related death investigations.

In 2014, the state Office of Children and Family Services investigated 284 child fatalities where abuse was suspected as a factor — up from 265 deaths in 2010, according to a report by the agency in February. The agency typically launches a review of all children who died while under the supervision of county child protective services workers.

Nearly half the 1,068 deaths investigated by the agency between 2010 and 2014 were caused by abuse and maltreatment, according to the report.

“These are children too young to realize they’re being neglected, too young to realize they’re being abused,” said Nassau CSEA president Jerry Laricchiuta. “They don’t have the resources that we do, so they rely on us to protect them.”

Cuomo’s office did not respond to a request for comment.

At the Nassau County Legislature’s meeting on July 11, Laricchiuta invoked the 2008 case of Leatrice Brewer, a New Cassel mother who admitted to killing her three children, to implore county lawmakers to reach out to Cuomo’s office in support of the bill.

A state probe later found Nassau child protective services workers conducted incomplete investigations and missed signs of abuse in the Brewer case.

Laricchiuta reminded legislators that a year before the siblings were found dead in their apartment, the union had complained to county leaders that workers were struggling to keep pace with caseloads of more than 40 per month.

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However, Nassau Social Services Commissioner John Imhof raised concerns about the measure. In an interview, he said “legislating caseloads may remove the flexibility needed” by the department to switch caseworkers between CPS and foster care cases, depending on which unit has a greater need.

Nassau has gradually increased the number of child protective services workers over the past five years. Currently, there are 64 workers, up from 58 in 2012, according to the county. The number of child abuse cases reported to the county decreased from 7,067 in 2011 to 5,779 last year.

In Suffolk, there are 91 child protective services workers — eleven fewer than in 2012, according to the Suffolk Department of Social Services. Last year, the department investigated 8,957 reports of child abuse and neglect, compared with 9,159 in 2012.

Daniel Levler, president of the Suffolk County Association of Municipal Employees, said the union has been working with its lobbyist and members to determine the “best plan” to generate support for the measure locally.

“When you don’t have the staffing levels that you need, people are overworked, things get rushed, and if mistakes happen, you’re talking about vulnerable children who are impacted,” Levler said.

A study by the state Office of Children and Families that analyzed caseload levels for the last six months of 2015 found that on average 33 percent of child protective services workers in Suffolk, and 22 percent in Nassau, had more than 15 cases at the end of each month. In 11 other counties the averages ranged from 50 percent to 67 percent.

Assemb. Donna Lupardo (D-Binghamton), who with state Sen. Martin Golden (R-Brooklyn) sponsored the bill awaiting Cuomo’s signature, said the variation between counties points to the need for a uniform state standard.

“It’s a very daunting task to be responsible for these cases,” said Lupardo, chairwoman of the Assembly’s Committee on Children and Families. “It’s very hard to recruit, train and retain these workers when it’s such a stressful position . . . I think if they knew they had a predictable work routine it would address some of the high turnover rates.”

Lupardo said the measure has not yet made it to Cuomo’s desk for review, but she expects it will be “called up” in the coming months.