Who is responsible for patient liability?

I think the safe thing to do would be to sign: Mary Smith, in her capacity as POA for John Smith.

If the patient is on medicaid I believe they have have a formula that tells how much the patient is responsible for. Our attorney has told us it's very important if your parent is ever admitted to a hospital and can not sign themselves in and you have to, always sign in with the parents name followed by "by your name". For example "Mary Smith by John Smith". If you just sign your name you are taking financial responsibility.