My father passed away can bank make me pay his neg. balance

I'm a little bit confused by your narrative. But, in general, family members are not responsible for a decedent's debts, the decedent's estate is.

Who was listed on the account card/account agreement as the "owner" of the account? If it was solely your father's account, and only he signed the account card/account agreement and you had no connection with that account, then the bank should not have any legal standing to pursue you (assuming there are no other unstated facts which would affect the situation). If, however, you were a joint-account holder/owner with your father, then you most likely signed an account agreement which probably created some obligation back to the bank. That cannot be determined without a thorough reading of the account card/agreement for that account. You may want to request copies of the account agreement and/or account card (different banks use different terminology) and take those to a qualified attorney for review.