To my understanding, there are no federal laws prohibiting employers from asking employees the reason for using a PTO/Sick day. In general, employees do not need to disclose the nature/extent of the illness/injury or any medical details unless they choose to do so. However, employers are allowed to understand the expected duration. So if you are sick, you only need to disclose you are ill. State laws vary, as do employer practices, or whether the employee belongs to a bargaining unit/organization (such as a Union - whereby other employee protections may be afforded)
My Employer's policy encourages managers not to ask for specifics related to a sick day being requested, in so far as sick days are available to be taken by the employee. At the same time, especially since most states are considered in some level of at-will work states, employees can be terminated for anything that isn't legally protected like FMLA / ADA or discriminatory in nature. So using a sick day inappropriately from stated employer policies - could lead to termination - if the employer feels this is necessary.