In order to recover for injury an individual must be able to prove that you were negligent. e.g. that you failed to peform some act that would have prevented the injury. There needs to be some determination that the stairs were in misrepair, or not properly maintained/designed to handle pedestrian traffic. In addition, you can only be sued for "common area". These are areas that are under your control. You should also check your lease for a "hold harmless clause." It is not applicable in many cases but may help you
Your insurance company should handle this. If not covered, you should contact an attorney. There are a number of defenses for this type of occurrence. You should inspect the stairway and make sure there is no dangerous condition such that another person can get injured.
Notice of the injury can occur much later than the occurrence. Timeframes of 1-2 years are not uncommon.
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