My father has a credit card. He added me as a additional card holder. He passed away. Can credit card company come after me?

If you have never filled out a card application or agreed to be contractually liable for the balances on the account, you have no contractual liability for the card expenses.  There are extracontractual claims which a the card company might be able to pursue; however it would be highly unlikely that the card company would undertake such actions.