CHICAGO (Reuters) - Illinois Governor Bruce Rauner vowed to pursue a legal challenge against union dues the state collects from non-unionized, rank-and-file government workers despite a U.S. Supreme Court ruling on Tuesday that upheld the practice. In a victory for labor, a 4-4 deadlock by the nation’s high court allowed a federal appeals court opinion to stand against 10 non-unionized California public school teachers who contended so-called fair-share dues should not be withheld from their paychecks if they chose against union membership. But the court move likely does not settle the issue, because nearly identical federal litigation in Illinois that Rauner helped launch last year remains viable. “Our case is winding its way through the courts, and it will get to the Supreme Court probably at some point in the future,” Rauner said during a stop in rural Illinois on Tuesday. “And we will just continue the fight for the freedom of political expression and the right of free speech for government employees. It’s a fundamental issue.” Since taking office in 2015, the first-term Republican governor has waged war with public-sector unions in a bid to weaken their longstanding influence over state politics. During his first month in office, the governor signed an executive order to bar state agencies from withholding fair-share dues, which non-unionized employees must pay under Illinois law and collective-bargaining agreements to support non-political union activities that benefit all workers. Public-sector unions sued in Illinois state court to block Rauner’s executive order from being implemented and persuaded a judge to allow the fees to continue to be collected while the case, which is still pending, was litigated. Simultaneously, Rauner sued in federal court to challenge the fees, but last May he was dismissed from the case by a judge, who ruled the governor lacked legal standing. Three non-unionized Illinois workers forced to pay between $19.75 and $60.86 in union dues per paycheck were allowed to proceed with their own complaint. A spokesman for the union representing the largest bloc of state workers called Tuesday’s Supreme Court ruling a “win” but acknowledged the Illinois case may become the next fair-share battlefront. “These attacks are political, and they’re ideological. They’re brought by people who want to rig the economy and our democracy in their favor. They’re not going to stop because they lost this particular challenge. They’ll bring another one,” said Anders Lindall, a spokesman for AFSCME Council 31. 