As observed in Garcetti v. Ceballos , the First Amendment limits the ability of a public employer to impose restrictions on employees in their capacities:

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In Garcetti v. Ceballos, the Supreme Court held that when public employees make statements pursuant to their official duties, they are not speaking as citizens for First Amendment purposes, and the Constitution does not insulate their communications from employer discipline. However, when they speak out as private citizens on matters of public concern, they are protected under the First Amendment, thus limiting the ability of public employers to restrict their speech in this capacity.

As Observed in Garcetti V