In a situation where a single structure contains many different independent owners, the liability for a burst pipe can be a confusing question. The cause of the break must be determined, and then liability would belong to the party which, intentionally or not, caused the damages. That person is responsible for repairing the broken pipe as well as any damages caused to other inhabitants of the rowhouse.
Ownership of the burst pipe indicates who is responsible for the damages it causes, unless the pipe was broken accidentally or intentionally by someone else. For example, if the pipe burst because of the other home owners did not perform their expected maintenance it would be that person's responsibility, but if the pipe burst because it was old, then the owner of the pipe would be liable for damages.
In some situations, the responsibility may fall on the local municipality. If the burst pipe belongs to or is on city right of way, then they would be the party to file a claim against, unless the damages, as before were caused by someone else.
If the broken pipe was caused by a child playing on the pipe or some other unintentional event, the liability goes to the person responsible, or their legal guardian in the case of a minor. You would need to contact that person and discuss the cost of damages and claim negotiation. In most cases, the responsible party would to file the claim, while your claim is filed against that person.