How do I garnish a Native American working at a Casino when I have a Judgment?

Native American Reservations are sovereign nations except where they have given away a part of that sovereignty; all reservation nations have signed agreements with the United States (it is required through agreements with the US Government and the BIA), and its subordinate states to recognize and enforce judgments from other courts (states) Uniform Enforcement of Foreign Judgments Act (UEFJA) of 1986. It should be noted that the Navajo nation will enforce orders from the United States (See Navajo Rules of Civil Procedure, rule 60 (Generally)).

Your first step is to contact the tribal entities office of the attorney general ((928) 871-6345) and ask them about the enforcement procedures.

If the order is for Child Support, then the federal government can and will get involved (IE: Garnish the whole tribe, in order to pay the judgment).

you cannot garnish any casino worker weather they are tribal or non tribal Indian reservation are considred a soverign nation so unless they get employed elsewhere not going to happen you could take them to court instead