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The Service Employees International Union (SEIU) Local 1000, which represents 95,000 state workers, says the new contract that takes away Columbus Day has not been ratified by the Legislature.
The union says until the new agreement is signed by the governor, it is operating under the old contract.
"We know it's a holiday, we know where we are legally because the so-called new contract has not been ratified, which shows this is a non-holiday," said Phyllis Johnson of SEIU Local 1000.
"I am asking that you do not quietly submit to allowing the state to take away our holiday," said SEIU president Yvonne Walker in a letter to workers. "I know that this is a big ask in light of the governor's imposed furloughs, but it is important because this is about power."
The chief deputy director of policy, Julie Chapman, sent a letter to the union, accusing them of encouraging an illegal work stoppage.
"SEIU's efforts on this issue can no longer be considered fair communication about your members' rights," Chapman said.
The governor's office said disciplinary action may be taken if workers do not show up for work, including termination and suspension.
"We told our members that if they are directed that, which many of them have today been directed to come to work, that there is not a holiday. And we said follow that order," said Dennis Alexander, Professional Engineers in California Government.
On the DMV Web site, it said its offices will be open all day on Monday, but a spokesman for the DMV said there were at least three offices in the L.A. area that closed because workers did not show up. Of the 168 DMV offices statewide, at least seven are closed.
The Glendale DMV office was closed, which was a surprise to many people who showed up with appointments.
The sign on the door said the closure was due to unexpected employee absences, but customers say the DMV should have been prepared.
"So this is a government office and I want to know why they didn't at least bring substitutes in that had worked here and had been laid off," said one customer. "I've been here since 12:30 and there have been a lot of people here that are very disappointed."
The same scenario played out at a number of DMV offices across the state.
In Oxnard, 13 employees called in sick, forcing the office to close for the day.
A DMV spokesman says they may dock the pay of those workers who didn't show up for work and may even take disciplinary action against them.
Meantime, the union says it will help its members file labor grievances against the state if their pay is docked.
Eyewitness News reporters Amy Powell and Jovana Lara contributed to this report.