"Inheritance" is generally not included as income....but some forms of income you receive when someone passes away can end up being income....what kind of inheritance are you referring to?
The person making the disclaimer needs to file a written and signed disclaimer with the person in charge of the estate, usually the executor or personal representative. It must be irrevocable and unqualified. If the reason behind the disclaimer is due to any potential legal problems, I would definitely consent an attorney rather doing this yourself. If I were doing this, I would consult an attorney for any such disclaimer.
And, at least around here, the disclaimer needs to be filed with the Register of Wills, who oversees the probate process. A state might have a particular form to use, too.
Since the question is being asked in a tax forum, I wouldn't assume that the probate process is involved. It might be an inherited IRA, in which case the IRA trustee would have requirements that would vary depending on the decedent's residence, and the trustee's residence. (Has anyone else run across Vanguard's paperwork two witnesses for a PoA, because Vanguard is in Pennsylvania and that's what is required there?)
I think for estate-tax purposes the disclaimer must be done within nine months of death, but you should look that up, if this involves one of the very few who pay estate taxes these days. It's more likely, that Grandma, age 85, left her IRA to Son, age 60 but recently diagnosed with terminal cancer -- he wants to disclaim it to the named alternate beneficiaries, his kids, ages 25 and 30.