There are generally two types of "per capita" payments, only one of which is subject to required federal income tax withholding.
When the tribe or any other payor distributes net revenues from their class II or class III gaming activity, income tax withholding is required. (See also FAQ #8 below);
Distributions that are not from Class II or Class III gaming activity do not require income tax withholding;
If the tribal member does not provide a Social Security Number (SSN), or if the IRS notifies the tribe that the SSN provided is incorrect or that another problem as described in Internal Revenue Code section 3406(a)(1) exists, backup withholding is required.