WASHINGTON >> A Supreme Court with a reconstituted conservative majority is taking on a new case with the potential to financially cripple Democratic-leaning labor unions that represent government workers. The justices deadlocked 4-4 in a similar case last year.

The high court agreed today to again consider a free-speech challenge from workers who object to paying money to unions they don’t support.

The court 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 latest appeal is from a state employee in Illinois. It was filed at the Supreme Court just two months after Justice Neil Gorsuch filled the high court seat that had been vacant since Justice Antonin Scalia’s death.

The stakes are high. Union membership in the U.S. declined to just 10.7 percent of the workforce last year, and the ranks of private-sector unions have been especially hard hit.

About half of all union members now work for federal, state and local governments, and many are in states like Illinois, New York, and California that are largely Democratic and seen as friendly toward unions.

The Illinois case involves Mark Janus, a state employee who says Illinois law violates his free speech rights by requiring him to pay fees subsidizing a union he doesn’t support, the American Federation of State, County and Municipal Employees. 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, that 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. Gorsuch was confirmed in April and the appeal was filed in June.

The justices will hear argument in the winter.