Yes, your son may be able to sue the community center in PA for his injuries. Under Pennsylvania slip and fall accident law, public establishments, such as a restaurant, community center, etc., have a duty to protect their patrons or members from unreasonably dangerous conditions. If a member or patron is injured due to a dangerous condition on the premises, the public establishment will mostly likely be found liable for the patron's injuries.
In order to prevail against the community center in Pennsylvania, we would need to prove that a dangerous condition existed and that the community center knew or should have known about it. A thorough investigation needs to be conducted to determine what caused the puddle of water to be on the locker room floor.
If the puddle of water on the floor was caused by rain coming from a leaky roof, then the puddle of water is a dangerous condition the community center likely knew about or arguably should have known about. If the community center knew about the roof leak from prior rain storms but failed to fix the leak, then it knew about it and will be held liable for your son's injuries.
Even if the community center did not actually know about the leaky roof but should have known about it, then the community center may still be liable. If employees were supposed to clean/inspect the locker rooms every 2 hours, but failed to do so, the community center will be liable because it would have known about the problem if its employees actually checked the locker rooms.
A related issue I want to touch upon is your son's age. If your son is a minor (under 18 years old), he will not be able to file a lawsuit against the community center. You or your husband, as his natural and legal guardian(s), will need to file the slip and fall accident lawsuit on his behalf. If you file a lawsuit on behalf of your son, you will have 2 years from the day of his slip and fall accident to file suit pursuant to PA's statute of limitations.
Your son, himself, can only file a lawsuit after he turns 18. In that case, the 2 year statute of limitations does not apply until he turns 18. Therefore, he has 2 years from the day he turns 18 to file a lawsuit against the community center.
If you have other questions, feel free to call my office to schedule a FREE consultation. 877.944.8396