Who is responsible for broken sprinkler pipe inside the roof in my unit

First, check the condo documents to see legally who is responsible for the maintenance of that pipe: you are almost certainly correct, in that this is the sort of thing that is almost always the association's responsibility, but since each condo is governed by its own legal documents, it pays to double check what they say in this case.
Assuming, as I am that the condo is responsible, the question because *why* did the pipe burst? If it was due to inadequate maintenance, or poor repairs done previously by association staff or contractors, the association should be responsible. On the other hand, if association had been doing the recommended amount of maintenace and keeping its infrastructure up, they may not be liable: the association is only financially responsible for damage to your unit, even if the damage comes from an area under their control, if they were at fault in some way in causing the damage. (For example: the association most likely maintains and is resposible for the roof, but if a heavy tree limb crashed through your roof during a severe storm, they would not be liable, since that is not their fault.)
At this point, while you suspect that lack of maintenance led to the break, you probably don't know that for a fact, unless you have some sort of insurance adjustor's report, or an analysis by a contractor or plumber who went in to do repairs, stating that. Therefore, bear in mind that it is most likely the case that you at present cannot prove the cause of the damage.
If they were not liable or responsible for the damage, then this is someting that should be covered by your own condo owner's insurance. Therefore, if you have the appropriate insurance, submit the claim to your own insurer--your insurer has much more expertise and resources than you do to determine who is at fault, and they *should* pay your claim, then themselves sue the association, if they believe the association was at fault, to recover the money they pay out to you ("subrogation"). This is why you have and pay for insurance--to cover losses. Take advantage of it.
If you don't recover through your insurance, while you can ask for the assocation to pay, you can't force them to unless you sue them and win. To win, you'll have to prove their responsibilty or fault for the loss, which may be difficult and could involve hiring your own expert to look at the damage and issue an expert opinion. Be advised that even beyond the cost of the expert, litigation can be expensive in cases like this--you will almost certainly need to hire a lawyer to have a reasonable chance of winning, and that  lawyer will likely have to spend many tens of hours on the case--and can take well over a year. Therefore, unless the association voluntarily agrees to pay you, the *only* inexpensive and fast way to get compensation is through your own insurer.