More budget cuts are coming to the already cash-strapped Judicial Branch, although it’s too soon to say what belt-tightening measures will be taken.

In a letter to the Judicial Branch and Office of the Chief Public Defender, Gov. Dannel P. Malloy said last week that officials must submit plans for a combined $5.7 million in spending reductions for the current fiscal year, which ends June 31. The reductions, which are part of a plan to reduce spending across all state offices, are necessary to close a projected $365 million budget shortfall for the current year, Malloy said.

“We know we need to be part of the solution,” Judicial Branch spokeswoman Rhonda Stearley-Hebert said. “We are working on specifics of the plan, so we are not yet in a position to provide details.”

Further cuts for the current year aren’t out of the question. By law, Malloy can only roll back 5 percent of agency budgets without legislative approval. And so his announcement last week covered only the first $171 million in spending reductions, including reductions of $32.2 million at the Department of Social Services and nearly $33.5 million in state employee fringe benefits costs.

The legislature will later be asked to make up the rest of the projected deficit for the year. Beyond that, there’s already a $1.2 billion projected deficit for the new fiscal year, which begins on July 1.

To comply with Malloy’s request, Judicial Branch officials were asked to submit a preliminary plan to the Office of Policy and Management by then end of this week. While it may be too early to say how the cuts will be implemented, court administrators have faced unexpected funding cuts several times in the past few years.

For the current fiscal year, the court system received $482 million, down from $511 million the year before.

Back in February, the governor asked the court system to make similar cuts, including what amounted to a $600,000 reduction to the budget of the Public Defender’s Office, which is on the state budget line at the Judicial Branch. Chief Public Defender Susan O. Storey could not be reached for comment last week.

In 2010, the Norwalk juvenile court facility and law libraries in Milford and Norwich were closed, to allow for a $13 million budget cut.

Last fall, hours at law libraries in Hartford and Waterbury were reduced because of a hiring freeze.•

The Associated Press contributed to this report.