If a additional cardholder is on a credit card is heshe responsible for deceased persons debt?

It depends. If the additional cardholder is designated ONLY as an authorized user, that is - that person's credit history was not used together with the decedent's credit history for the original credit line - then no, because the credit line is linked only to one social security number. If the additional cardholder applied as a co-applicant (not added as an authorized user) with the decedent for the original credit line - then more than likely, yes. Individual state laws take precedence. Ask for an original copy of the contract from the creditor to be sure.