Lawrence has made some great points. I don’t own a gym, but if I did, I would develop a safety policy covering the gym and my business in general. I would speak with an attorney first. From there, I would follow his/her suggestions as to where to post the rules and guidelines as well as include them in the membership contract. I believe when a member sings up for a membership, that is the best time to explain he rules and guidelines that must be followed. I would also include safety rules and regulations into your SOPs (Standard Operating Procedures) so they apply to employees as well. Include them in your employee manual and have employees sign a document acknowledging receipt of the manual and its contents and agreeing to abide by them. Be sure you post them in an employee break room or wherever your other employee-only postings are.
First and foremost when it comes to protecting your gym or PT studio/business, speaking with a lawyer in the jurisdiction where your business is located is best. That way they can advise you of the specifics, if any, are needed to be placed in a member agreement/contract.
I am a gym owner and not only do I place safety notices in the membership agreement, I also have the member go through the gym with a staff member at orientation and demonstrate to them safety issues with equipment, their responsibility of re-racking the equipments and their part in equipment cleanliness (using a towel & wiping down equipment after use). I also place in the safety notices where emergency features are located, request their respect toward other members and staff and notify them that inappropriate behaviors will not be tolerated. Additionally, age requirements are noted.
I hope this is at least a helpful start. If you have any specific questions, I would be happy to answer them to the best of my ability and expertise.
For more Gym Business Insights, I have a blog that you can visit that will also help out with issues that gym owners deal with.