If it's a pipe that supplies steam and water to your coop it is the coops problem to fix and repair all damages.
I would also contact your insurance company to come and inspect the damage as the coop insurance company should also be contacted via the managing agent/board. Best of Luck

Who is ultimately responsible should be spelled out in your Proprietary Lease. There is no law or regulation governing damages, so you will be guided by your PL.

The first thing I would do is take photos of all the areas with damage. Get a lot of pictures ranging from long distance views to establish the relationship of the damaged area(s), to close-ups of each damaged area. Take lots of pictures from all distances and angles. Film is cheap, and you never know when one angle and lighting condition shows something that other pictures don't.

Take pictures of all appliances, clothing, decorations, artifacts, electronics, etc that were damaged by the burst pipe. You will want to submit them as part of your claim. If any had value as collectibles you'll want to get the receipts or appraisals to verify their value.

Next, contact *your* insurance carrier who has your individual co-op/condo owners' insurance policy, and open a file with them about your loss. Schedule an appointment with the adjuster they specify for as soon as possible.

If any part of your apartment is unusable or uninhabitable, discuss with your insurance company what you should do. You shouldn't have to live with, say, a bathroom ceiling that is about to fall down.

*Do Not* discuss the loss with anyone connected with your board, their insurance carrier, and adjuster, etc. You have an obligation to allow your board's adjuster access to your apartment and all damaged area, but you are under no obligation to give a statement or answer any question no matter how innocuous. In those instances, simply refer them to your insurance agent or representative.

Make a copy of your Proprietary Lease. Your insurance agent will most likely ask for one so they know how to apportion responsibility.

This could become a slog, so be prepared to wait and deal with the frustrations. Good luck!
--- Steve

The coop management called in a contractor to estimate the damage and have started repairs ~30days after the incident. I did not have to go through my own insurance.

Glad to hear that the co-op did the right thing.

Congratulations on getting this resolved with a minimum of aggravation. You have a very good board.