In Florida, you cannot be held responsible for a spouse's credit card as to which you were not a co-applicant. There is some law which could hold you responsible if you were an authorized user to the extent of the use of your credit card. However, if you didn't have a card and didn't know it existed, you are not liable. Franky, this happened to my mother after my father passed away. I would send a certified letter, return receipt, advising of these facts and disputing the debt and advising the creditor to cease all communications with you pursuant to the federal Fair Debt Collection Practices Act or you will pursue them in federal court for violation of the statute. After a few such efforts, in my mother's case and in the case of another client, this stopped all efforts to collect.
You should not be responsible for these debts if you did not sign for them or use them. Why do you ask? Are they trying to get you to pay them? Do not agree to anything and do not make any payments. You should also obtain free copies of your credit reports from the website linked below to see if these debts are appearing on your credit reports. If so, you must dispute the debts as explained on my website, also linked below. Keep a detailed log of all contacts with the creditors if they are contacting you including the name, phone number, date and time of call and what was said. There are laws that govern debt collection that provide for damages and payment of your attorney's fees if they violate these laws
What was the credit card used for? If it was used for medical debt, in many states, the wife could be held legal responsible for paying it. Why? Well, remember those wedding vows, "for richer, for poorer, in sickness & in health?" Many states interpret those vows to mean you will pay for your spouse's medical care, whether or not you agreed to it, and whether or not you know about it.
Otherwise, creditors only know who signed the application for credit. They don't know & they don't care about the spouse unless the spouse signed the application. However, if the creditor obtains a judgment, any joint assets, such as real estate, bank accounts, vehicles, etc., could be attached, so this isn't the easy question that you might have expected.
Hope this perspective helps!