Following the drop-off of three dozen children at Nebraska hospitals under an open-ended safe-haven law, many state senators support an increase in services for older kids with behavioral problems.

But a significant number are also unsure whether a new slate of services is really the right answer for problems some say were strikingly illustrated by the two-month-long drumbeat of child drop-offs at Nebraska hospitals this fall.

“We need to make sure that the services that we have are being utilized,’’ said Sen. Arnie Stuthman of Platte Center, one of those who is unsure.

In a pre-session survey of lawmakers by The Associated Press, 22 said the state needs to increase services for older children. Twelve said they were unsure and two said no. Two senators skipped the question, two others gave other answers and nine senators did not participate in the survey.

“The safe haven highlighted the concerns we should have regarding services for older children with behavioral problems,’’ said Sen.-elect Galen Hadley of Kearney, one of those who supports an increase in services.

Earlier this year, Stuthman introduced the safe-haven bill that was designed to protect newborns from being dumped in trash bins or worse. The Legislature amended the bill so that it didn’t have an age limit on children who could be dropped off at hospitals.

The consequences stunned state lawmakers and people around the country.

Thirty-six children from as far away as California and Florida were abandoned at Nebraska hospitals. None were infants, and most were preteens and teenagers as old as 17.

So state senators met in a special session in November to change the law, limiting it to children 30 days old or younger.

Afterward, a task force of lawmakers was formed to study the issue of services for older kids and give recommendations to lawmakers. The group hasn’t formally released recommendations, but is considering a hotline that desperate parents could call for help and round-the-clock information and referrals provided by each of the state’s six behavioral health regions.

Several senators said in survey responses they wanted to wait for the task force’s recommendations before deciding whether more services are needed.

Looming above senators as they possibly consider helping kids is a projected state budget shortfall.

Some senators said they might support dipping into the state’s cash reserve if needed.

“If increases in services cannot be covered by existing programs, the cash reserve must be viewed as a funding source,’’ said Sen.-elect Colby Coash of Lincoln.

Others didn’t mention the state’s rainy-day fund and said the state should look for savings in other areas to help pay for help and determine if money in existing programs should be shifted to help older kids and their families.

“We need to prioritize programs within Health and Human Services and take funds from programs that aren’t working and use those moneys to support successful programs and strengthen areas that need more attention, like behavioral health,’’ said Sen. Tim Gay of Papillion.