Do I have to prove what caused my slip and fall?

In a personal injury case, you are the plaintiff and have the burden of proof in establishing negligence on the part of the hospital for the slippery floor.  You don't have to identify the exact item that made the floor slippery. 

Without an accident report and the names of the witnesses, it may be difficult to prove that you slipped and fell at the hospital.  The hospital's insurance carrier might claim that you slipped and fell elsewhere and deny the claim. Were there any warning signs, cones, etc. about the slippery/ wet floor?

Negligence is the failure to exercise due care (that degree of care that in this case a reasonable hospital would have exercised under the same or similar circumstances to keep the floor clean and prevent foreseeable harm).  In order to prove negligence, you will need to prove duty (of due care) mentioned above, breach of duty (failure of the hospital to exercise due care by not having the floor wiped up), actual cause, proximate cause and damages. 

Actual cause means but for the hospital floor being slippery, would you have fallen?  If the answer is no, actual cause has been established.  Proximate cause means were there any unforeseeable, intervening events which would relieve the hospital of liability?  If the answer is no, proximate cause has been established.

Damages means the amount of compensation you are seeking in your lawsuit.  Your damages would include your medical bills, pain and suffering and wage loss.  Compensation for the medical bills is straight reimbursement.  Compensation for wage loss is straight reimbursement.  Compensation for pain and suffering is an amount in addition to the medical bills.  The medical reports will document the nature and extent of your injury and will be used to determine compensation for pain and suffering.

Prior to filing a lawsuit for negligence against the hospital, it may be possible to settle the case with the hospital's insurance carrier.  Your claim would include the medical bills, medical reports, and wage loss documentation.  If the case is settled with the insurance company, NO lawsuit is filed.  If you are dissatisfied with settlement offers from the insurance company, reject the settlement offers and file your lawsuit for negligence against the hospital.  If the case is NOT settled with the hospital's insurance carrier, you must file your lawsuit prior to the expiration of the applicable statute of limitations or you will lose your rights in the matter forever.