Unless it's simplified in the lease, the landlord is responsible for repairs to the structure of the building. To be absolutely sure, you can find out about landlord/tenant laws through the courthouse or the BBB. Hope this helps.
If the roof of your place is leaking and the seepage is damaging the walls the best thing to do is for you to get a plumber to come over and check out the cause of the leakage and to give you an estimate of the cost of repairs. Secondly you should immediately inform the landlord and he or she may have their own plumber who can estimate the damage. You should check your tenancy agreement as there will be a clause that specifies what are your and the landlord's liabilities.
Normally the tenant is responsible for minor repair work and it's only in case of structural damage etc that the landlord becomes responsible. The best course of action is to inform the landlord about the problem. Get his or her advice as to how to get the problem fixed and who will be responsible for paying for the repair work and then getting the place fixed. In certain cases the landlord has an insurance of the place which covers for major repair works and will only want to file an insurance claim if the cost exceeds a certain amount. It may also be possible that your landlord may work out some agreement by which both of you share the repair cost but this really depends on the kind of relationship that you have with the landlord.