* Case involves legality of fees non-union members must pay
* Supreme Court deadlocked 4-4 in similar case in 2016 (Added details on states in which agency fees are mandatory, unions' "free rider" argument, paragraphs 10-18)
WASHINGTON, Feb 23 (Reuters) - The U.S. Supreme Court on Monday will consider for the second time in two years whether to choke off a critical funding stream for public-employee unions, potentially reducing organized labor's influence in the workplace and at the ballot box.
The nine justices will hear a challenge backed by anti-union groups to the legality of fees that workers who are not members of unions representing teachers, police, firefighters and certain other government employees must pay to help cover the costs of collective bargaining with state and local governments.
Two dozen states require payment of these so-called agency fees, covering roughly 5 million public-sector workers, that provide millions of dollars annually to unions. Their disappearance would deliver another blow to a U.S. organized labor movement already in a diminished state compared to past decades.
The justices considered a similar case in 2016, and after hearing arguments appeared poised to overturn a 1977 Supreme Court precedent that let unions force non-members covered by contracts negotiated by organized labor to pay fees in lieu of union dues to help cover non-political union expenditures.
But the death of conservative Justice Antonin Scalia the following month left the court with an even split of conservatives and liberals, and its 4-4 ruling in March 2016 did not resolve the legal question.
Republican President Donald Trump's appointment of Justice Neil Gorsuch last year restored the Supreme Court's 5-4 conservative majority. Gorsuch could cast the deciding vote in dooming agency fees.
Depriving unions of agency fees could hamstring their ability to spend in political races. They typically back Democratic candidates over Republicans.
The 2016 case was brought by non-union California public school teachers. The plaintiff in the current case is Mark Janus, a child-support specialist for the state of Illinois who opted not to join the union that represents employees like him, the American Federation of State, County and Municipal Employees (AFSCME).
In both cases, the challengers argued that being forced to pay the agency fees to unions whose views they may not share violates their rights to free speech and free association under the U.S. Constitution's First Amendment.
Unions in both cases contended that mandatory agency fees are needed in order to eliminate the problem of what they call "free riders" -- non-members who benefit from union representation, for example through salary and working conditions obtained in collective bargaining -- without actually paying for it.
'I LOSE MY JOB'
Janus, 65, is backed in the legal fight by anti-union groups including the National Right to Work Legal Defense Foundation.
He said in an interview he is not a member of a political party and his objection to the fees was not based on politics. Janus said he has chafed at having to pay the fees, currently just under $50 a month, since starting his current stint working for Illinois in 2007.
"I don't agree with the fact that someone is telling me I have to support something without asking me about that. This is not freedom of association. If I don't pay, I lose my job," Janus said.
AFSCME and other public-sector unions have called the case a well-funded attack by corporations and billionaires to undermine organized labor.
"This case is about power," American Federation of Teachers President Randi Weingarten said.
"The funders of this case want a new Gilded Age, this time on steroids," Weingarten added, referring to a period in the late 19th century known for its concentration of wealth among industrialists.
Twenty-four states have agency fee requirements. While 28 states have so-called right-to-work laws that prohibit mandatory agency fees, Wisconsin and Michigan have exceptions for police officers and firefighters that permit agency fees covering those workers. In those right-to-work states, unions still represent workers but membership rates are lower.
Federal employee unions cannot collect agency fees.
The union membership rate among public-sector workers was nearly 35 percent in 2017, more than five times higher than the unionization rate for workers in the private sector, U.S. Bureau of Labor Statistics figures show. The case does not affect private-sector unions.
Taking away mandatory agency fees could have profound implications for public-sector union coffers. Unions in New York state, for example, would lose an estimated $110 million per year without mandatory fees from non-members, according to the business-backed Empire Center for Public Policy.
(Reporting by Robert Iafolla and Lawrence Hurley; Editing by Will Dunham)