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Last week, top administrators ordered them to stop wearing union symbols in public to avoid an appearance of bias.
"While we understand the right to participate in negotiations and union activities, we also require conduct that does not compromise the appearance of neutrality and impartiality to the public and other court users," Court Administrator Denise Gordon said.
On Tuesday, union representatives sent a complaint to the state Public Employment Relations Board, which will evaluate it, said SEIU field representative Kris Organ.