First - if you have been injured at work then you have a workers compensation claim. This is a claim against your employers insurance that will pay for a certain amount of lost time and medical care. Depending on your injury you may eventually receive additional money at the end of the case.
As to suing, you cannot sue your employer in general, but if someone else was responsbile for maintaining the stairs or there was a defect, etc. then you may be able to bring an action against that 'third' party.
You should definitely seek legal counsel.
EVERY case is different. The answers provided here are general and not related to the specifc facts of your case. I am not your attorney and if necessary you should seek legal counsel. This answer is NOT to be considered legal advice and there is NO attorney client relationship implied from this answer.
Your workers compensation benefit is your exclusive remedy unless your injury was caused by someone who does not share the same employer. That is if your fall was the result of bad construction or faulty maintenance by someone other than your employer you may be entitled to bring what is commonly referred to as a third-party action. Absent such circumstance you are entitled to wage replacement benefits and medical treatment in the workers compensation case.
The duration of your workers compensation benefits and the amount will depend on a number of factors including whether or not you are able to make money a different job.
Seek a local workers compensation attorney to review the facts circumstances of your case and to give you advice as to how to proceed. Absent all the facts and circumstances I cannot predict the amount of your benefits, the duration of your benefits or with the ultimate outcome may be.
Please remember the answer to this question is in general and without knowledge to the specific facts of your case. You should not rely on this answer when making important life decisions and seek a legal opinion based on your particular facts and circumstances.
Depending upon the cause of your fall it is very possible that you would have a third-party personal injury claim against the owner of the building where you fell. This would be true only if the owner of the building is different from your employer, meaning that if your boss on the building you can't sue.
If your injuries are significant enough to keep you out of work for a long stretch of time there certainly may be a case worth pursuing. I suggest that you immediately contact a local personal injury attorney. It will cost you nothing and you will have a better sense of your rights after your consultation.
The aforementioned opinion does not constitute legal advice and is for general educational purposes only. See an attorney licensed in your jurisdiction for competent legal advice. No attorney-client relationship has been formed through the within legal question and answer session.
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