can sue my landlord for a slip amd fall injury

You can sue anyone for anything, but the real question is what type of a case do you have? Most  people think that if you slip and fall or trip and fall on someone else's property, that there is automatic liability. The laws vary from state to state. Ordinarily, you have to prove your landlord was negligent for your accident; what did they do wrong that made you fall? Was the staircase defective in some way or poor lighting conditions to contribute to your fall? Was the bannister or hand railing defective? Do you have photographs showing the defect or witnesses who would testify as to what made you fall? From a practical perspective, does the landlord have homeowner's insurance that you could recover if you pursued your case? Insurance companies routinely deny liability on these type of trip and fall cases which will force you to file a lawsuit; you should consult with an experienced personal injury lawyer first to see if they feel you have enough substance and evidence to how your accident happened, in order for you to be pursuing the case.