I always do for a personal training client. Part of my contract are an Informed Consent, a medical, an exercise history and a physician’s approval, if necessary. The contract spells out my obligations and that of the client, a cancellation policy and the payment arrangements.
I also conduct MELT group classes from time to time which are not personal training. For those, I only require the completion of an Informed Consent.
under Home find a trainer
search by location city and state
filter results by cost, specialties, your interests….
contact the people that match your needs and ask these questions in that email
Most of the trainers I know do use a service agreement, though it may differ in how it is done if they are independent or if they work for a company. The best answer you will get is to find people you are likely to hire…. in your area, in your price range, with the experience and skills you need, …. and question that group about policies and pick the one that works best for you.