Employees are not required to divulge their vaccination status. However, if they do not, they must wear a mask.
Employers can ask employees to attest that they have been fully vaccinated. Employees who attest to being fully vaccinated may go mask-less. An attestation is different than providing your vaccination card or medical records. Employers limit their inquiry by only asking for attestations to avoid HIPPA or other legal issues because you have a right to keep your medical records private.
Policies and government orders are rapidly changing, so keep in mind that rules this week may not be rules next week.