Sorry to hear of the loss of father and your tax issues.
First, please know that there is not any income tax
on the inheritance but only on the income from the house, if you rent or when you sell.
As to state taxes, you will include the gain from sale of the house in your Georgia return since you have to include income from all states in your resident return. You will also file a California return since the property is located in California.
But you will not have to pay double because with your Georgia return you will get credit for the California tax paid on Form 500 Schedule 2 line 1.
In almost all cases, a personal residence that is held in a trust still gets the increase to the value at the date of death. When the trust is revocable during his life, your farther was deemed the owner of the house and the trust did not file any tax returns
itself. Your father included the income from any trust items just as if there was no trust for tax purposes.
Even with an irrevocable trust that had to file trust tax returns during his life, there is still increase in basis to fair market value when the house is included in the estate of the deceased.
So, the gain will most likely only be any change in value between the date of death and the date of sale.
Also, you may be aware that the gain on a primary residence is not included in income when the property is owned and occupied for two years out of five prior to the sale of the residence.
"Under new Section 121(d)(9), an estate or heir can exclude $250,000 of gain if the decedent used the property as his or her principal residence for two or more years during the five-year period prior to the sale.
In addition, if an heir occupies the decedent's home as his or her principal residence, the decedent's period of ownership and occupancy can be added to the heir's subsequent ownership and occupancy in calculating the two out of five years ownership and use test.
Under Section 121(d)(9)(C), the $250,000 exclusion is also extended to property sold by a trust provided that the trust was a qualified revocable trust, as defined under Section 645(b)(1), immediately prior to the decedent's death. Any period of occupancy and ownership of the decedent can be extended to an heir's subsequent ownership and use regardless of whether the principal residence was owned by a trust established by the decedent."
If you do not plan to sell the house soon you may want to consider making it your primary residence and then selling as your father's ownership and occupancy can be added to your subsequent ownership and occupancy for the two of five year test for excluding any gain on sale.
When you state that "She has elected not to file an estate tax return for the trust after my father passed" that likely means that your father did not have an estate large enough to be subject to estate tax and that there was less than $600 income in the estate for the year following his death. Estate tax returns, like others, are not optional or by choice.
Without access to the trust agreement and all the facts in your situation it is not proper for me to guarantee you have no gain but the rules
do allow for exclusion and for the increase in basis on the inherited property in almost all cases.
Hopefully this gives you good general information to begin to consider the tax issues. Although you can inherit without a lawyer it is probably well worth getting an enrolled agent, or other experienced tax professional, to properly apply the tax rules
to your specific situation and the terms of the trust agreement that your father had.
Please do ask if you need more discussion or clarification.