This really depends on who is on title. If both husband and wife were on title, in most cases all you need to do is contact your mortgage service provider and let them know this happened. They will have you fax in a copy of the death certificate and in most cases will take the deceased off the mortgage.
I do know of a few cases where they ran credit on the living borrower. And in todays times,I would not be surprised if they require you to fill out a short application.
The main question you need to ask yourself is what is the purpose of taking the deceased off the mortgage? It will cost some money as the title might need to be changes. In most cases the county court of clerks are going to charge a per page fee to record the new title.
If you are going to refinance, you can do this all at once.
You first need to find out how the property is currently vested.
More often than not, title is held as “ Joint tenants with right of survivorship”, this allows two or more natural persons to create survivorship rights through holding title to property. Interests must be equal among the co-owners and may be sold, gifted, or deeded during an individual owner’s lifetime. An owner may not dispose of a joint-tenancy interest in property by will inasmuch as the survivor(s) automatically own(s) the decedent’s interest upon the decedent’s death.
Contact your local Title Company and ask them to research the vesting. If it is possible for your situation, they should be able to do it for you.