What to do regarding water damage in my co-op?

Question Details: Have water damage from upstairs neighbors sink overflow no fault of building. It's a co-op buildingand both us are shareholders. I'm assuming the neighbors insurance should cover my damage question is how do actually get confirmation that they will? Most say that my insurance company will go after them to recover since it is covered however my coverage amount is minimal compared to what the repair work will be my agent has already told me they would only try to recover the amount which I'm covered under my policy. Do I contact the neighbor, contact the neighbors insurance directly I have the info, only discuss with the building or wait and go through a lawyer?

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