I live in Indiana and my husband died recently. Am I responsible for his past medical bills? I did not sign anything for his surgeries.

The best answer is "possibly." At common law, a person is liable for the "necessaries" of of his spouse, although this principle is rarely applied these days. As a practical matter, you will likely have success in resisting the claims of your late husband's medical creditors. When and if such claims are asserted against you, you should consult an attorney.