What is the name of your state (only U.S. law)? SC
I want to know if it is legal for one person on a joint checking account to close the account and take the all the funds and open a new account under their name only.
It depends on how the joint account was set up.
If the account was listed as John Smith OR Mary Smith, then yes it is legal since either person could siign without the other's signature.
However, if the account was set up as John Smith AND Mary Smith, no it would not be legal since both signatures would be required. That couldn't normally happen since the bank teller should catch that one signature was missing.