You may have a case. These cases are often brought by tenants against landlords.

Under the law in Massachusetts, landowners have a duty to remove snow and ice from exterior staircases. This is an exception to the unnatural accumulation theory of recovery. Of course, the fact that you fell on an exterior staircase does not make a case. Other facts must be established showing that the landowner failed to comply with his/her obligation to remove snow and ice from the staircase that you fell on, and, that his/her negligence is greater than any comparative negligence on your part.