At least one courthouse in each county will be open to the public if the state government shuts down, but services will be limited, a court official said Thursday.

That will leave about half of the state’s 36 courthouses closed for business.

Counties with more than one courthouse may rotate which days certain courthouses are open. For example, District Courts in Houlton and Fort Kent would be open Monday but closed Wednesday. District Courts in Presque Isle and Madawaska would be open Wednesday but closed Monday.

People should check the court website or call courthouses to learn when they will be open, State Court Administrator Ted Glessner said Thursday in a preliminary memorandum to court personnel. A final memorandum would be issued late Friday if a budget compromise cannot be reached.

Courts will hear cases that raise constitutional and/or health and public safety issues, Glessner said.

The judiciary is a separate branch of government from the executive and legislative branches. Technically, any order Gov. Paul LePage might issue concerning a shutdown would not apply to the judiciary.

But without a state budget, the courts don’t technically have the funding to operate, said Leigh I. Saufley, chief justice of the Maine Supreme Judicial Court.

“In those circumstances, each branch is only authorized to spend money for services deemed essential during an emergency,” she said. “Complicating the situation in the courts is the fact that, in many cases, executive branch employees or agencies are parties and will be unable to participate.”

Criminal matters such as arraignments, dispositional conferences, motion hearings and jury trials where a defendant or juvenile is in custody would be handled. Arraignments, scheduled motions to amend bail or probation and murder trials would go forward even if a defendant is not in custody.

It was unclear Thursday whether the governor would order prosecutors to stay on the job or not. Judges would not be able to preside over criminal cases without them.

Grand juries scheduled to convene during any shutdown would do so, the memorandum said.

The following civil and family matters would be addressed:

— Petitions for protection from abuse and harassment orders.

— Some child protection matters, including requests for preliminary protection orders and child jeopardy hering.

— Mental health commitment hearings and involuntary treatment proceedings.

— Civil injunctive relief addressing life or safety.

Divorces, evictions, small claims, foreclosure, traffic and other civil violations would not be heard.

The Maine Supreme Judicial Court and the Business and Consumer Court would be shuttered. The drug courts would not convene during a shutdown.

In addition to courthouses being closed, online services to pay traffic tickets and court fines will not be operating during a shutdown. People would be able to pay fines in person at open courthouses if that is where the fines are owed, according to Mary Ann Lynch, spokeswoman for the court system.

It has not yet been decided if late fees would be waived for people who are unable to get to a courthouse to meet a fine deadline.