WASHINGTON — Its conservative majority restored, the Supreme Court said Thursday it will return to an issue with the potential to financially cripple Democratic-leaning labor unions that represent government workers.

After the justices deadlocked 4-4 in a similar case last year, the high court will consider a free-speech challenge from workers who object to paying money to unions they don’t support.

The court, with conservative Justice Neil Gorsuch on board, could decide to overturn a 40-year-old Supreme Court ruling that allows public sector unions to collect fees from non-members to cover the costs of negotiating contracts for all employees.

The union fees case is among nine new cases the justices added to their docket for the term that begins on Monday. Others deal with a defendant’s right to direct his own defense, police searches of vehicles and overtime pay for service advisers at car dealerships.

Labor unions have been under sustained attack at the high court in recent years. The latest appeal is from a state employee in Illinois. It was filed at the court two months after Gorsuch filled the seat that had been vacant since Justice Antonin Scalia’s death.

The Illinois case involves Mark Janus, a state employee who says Illinois law violates his free speech rights by requiring him to pay fees to subsidize AFSCME, which represents tens of thousands of Illinois workers. About half the states have similar laws covering so-called “fair share” fees that cover bargaining costs for non-members.

Janus is seeking to overturn a 1977 Supreme Court case, Abood v. Detroit Board of Education. It said public workers who refuse to join a union can still be required to pay for bargaining costs, as long as the fees don’t go toward political purposes. The arrangement was supposed to prevent non-members from “free riding,” since the union has a legal duty to represent all workers.

A federal appeals court in Chicago rejected Janus’ claim in March.