Would an employer be responsible for paying an employee overtime if their physical therapy for a worker's comp case is schedule outside of their normal shift?

Under the law, an employer only has to pay overtime when an employee "works" more than 40 hours in a workweek. Time in physical therapy is not work for this purpose, even if the employee is compensated for it, just as vacation, sick and paid holiday time is not work for overtime purposes. (For  example: employee A takes sick days Monday and Tuesday, 8 hours each; then works 12 hours each Wed, Thur, and Friday. The employee will be paid for 54 hours--but since he/she only worked 36 hours, there is no overtime.)

Unless and only when the employer works more than 40 hours in a week, the employer does not have to pay overtime. It is free to be more generous if it chooses, but is not required to provide overtime under the circumstances you described.