Basis adjustments to property are the same whether the property is held by an individual or a trust.
First, depending on the language of the trust, the home may have acquired a stepped up basis equal to the fair market value on the date the previous owner died. This may require a real estate appraisal.
Then permanent improvements further increase the basis, but not repairs. (And, only improvements after the date of death. Any improvements before the date of death are rolled into the stepped up basis.) There are also a few closing costs that adjust the basis. These are listed in publication 523 beginning on page 8.
https://www.irs.gov/forms-pubs/about-publication-523
If for some reason, the house does not get a stepped up basis, you would start with the owner's basis and make any adjustments since that basis was determined. The owner's basis might have been set when they bought the home. If they co-owned the home with a spouse who pre-deceased them, they would get a partial or full step up depending on what state they lived in. You may need to have the trust documents reviewed by an attorney to confirm whether or not the house got a stepped up basis on the date of the owner's death.
