State law governs whether employees are permitted to review their personnel files. Some states, such as Michigan, have specific laws regarding when and how employees may access this information. Other states, such as New York, have no statutory guidance one way or the other.
Where there is no statute requiring access, employers can set up guidelines for employees' access to personnel files as they determine appropriate. It would be prudent to include those guidelines in the company’s employee handbook.
You should be familiar with the law governing the jurisdiction where your company is located. Employers with locations in more than one state should be aware of the rules applicable to all of their locations. If they want a policy that is consistent for all facilities, they should choose the rules of the state that are the most favorable for their employees and apply that universally.