As noted, you would handle the method for making the pay out according to state law. IRS regulations focus on calculating the required distributions, not on identifying the proper recipient or the documentation you would require before distributing the funds.
However, prior to distributing the funds, I suggest you review the last article of your IRA agreement to see if the payee might be someone other than the decedent's estate.
The IRS' model IRA forms leave the last article blank in order to allow the custodian/trustee to add any additional terms it regards as appropriate. Forms vendors routinely insert language which reflects their judgment and experience. Your IRA agreement may very well indicate who is to receive the funds if the IRA holder dies without effectively naming a beneficiary.
However, not all forms vendors have the same judgment and experience. Most vendor forms say that the funds would be payable to the decedent's estate. However, I have seen two that spelled out a line of succession beginning with the decedent's spouse, then the decedent's children and so on.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.