My mom, grandma and I are co owners of a co op. Our name is on the certificate. Is that enough to prove ownership if one of us pass?

Co-ops are an interesting form of ownership because they have two parts to them; a stock certificate and a proprietary lease.  The stock certificate provides legal ownership as far as inheritance is concerned.  For example, if the stock certificate shows your name, Mum's name and Grandma's name as joint owners with rights of survivorship and Grandma dies; you and Mum will automatically own all the shares.

But (and here is the wrinkle) share ownership does not give you the right to live there.  You still have to be approved by the co-op Board to go onto the proprietary lease.  Your finances will be inspected and you will be interviewed.  There are plenty of examples of co-op owners who are not able to live in apartments they have inherited because they cannot pass the Board.

As a further wrinkle, if this is in NYC, the co-op has to follow rental law.  So, for each person named on the lease, one other adult can live there as long as the person named is also in residence.  So Mum might be approved and that would allow you to live there with her even if you were not qualified.  But once Mum dies you would have to either qualify or leave.

The certificate will state the percentage of ownership in the corporation, but it may not show the percentage of ownership of each individual.  You would own stock in the corporation, but unless the certificate shows exactly how many shares each individual owns, then you can't know exactly how the passing of a deceased owner's shares will go. You need a attorney familiar with co-ops to answer this

What certificate? The certificate of health, proving that you are in compliance?