Denver Health spokeswoman Dee Martinez declined to comment on the lawsuit, saying officials there have not seen it.
In the lawsuit, the Service Employees International Union said some nurses began talking about joining a union last year.
In November, managers and supervisors began questioning employees about unionizing activities, warning them against it "and generally creating a culture of fear and an impression that defendants were monitoring and would retaliate against employees who joined, supported or even discussed anything about a union," the lawsuit said.
At least one employee's job was threatened after trying to discuss with a manager an open letter to nurses encouraging the organization activities, the lawsuit said.
It said Denver Health chief executive Patricia Gabow told employees in February that they weren't allowed to join a union because the hospital is a government subdivision, the lawsuit said.
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