I am sorry for your loss. You will be liable for any debts you and your spouse entered into together, including medical expenses if you also signed the agreement to pay for the expenses.
Under the laws of many states, a surviving spouse is responsible to pay for any "family expenses" of the couple or any expenses for the deceased spouse that the surviving spouse agreed to in writing or that the surviving spouse ordered for the deceased spouse. There is case law that says that a spouse's hospital and medical expenses are a family expense. If you were separated at the time the bills were incurred it may be a different story. Ask an attorney in your area.
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