In short, no, you don't need to have a specific policy on service animals for your workplace. If a request comes up, or an employee conveys that they need to have a service animal in your workplace, you should utilize your reasonable accommodation policy and engage in the interactive process.
The interactive process will help you determine if the employee has a covered disability, as defined by the Americans with Disabilities Act (ADA), and if a service animal is a reasonable accommodation. You may ultimately deny the request if the interactive process reveals that the employee is not considered disabled under the law, the animal doesn’t fit the definition of a service animal, or the animal’s presence would create an undue burden. If you’d like more information on reasonable accommodation policies, or the interactive process, we have many resources available on the HR Support Center.