I would believe that this could fall under "deadly weapon" or "dangerous weapon" territory, and nearly everywhere has some sort of law against the carry of those. If you are somewhere where there is a valid use for it (ie. hiking or camping), I have a feeling that it would pass muster (If confronted by LE I would refer to it as a hatchet or camp axe, and not a tomahawk), but having it strapped to your belt while at the mall doing Christmas shopping would likely lead to issues. And I have a feeling you would be in a world of hurt if you ever defended yourself with a hawk, if personal protection is what you're after it may be much more prudent to get a production hatchet and then make any modifications you want to it, and think of innocous reasons for say mounting a spike to the back of the head.
One loophole, at least in Michigan, allows re-enactors or actors participating in theater to carry crazy stuff like this, and there are also exceptions for double edged stone knives for primitive archers and re-enactors. If you want to dress up like a period mountain man, and could convince LEOs that you were just on your way to give a talk to some schoolchildren about early American settlers, you could also likely get away with it.
/I am not a lawyer
//my advice is worth exactly what you're paying for it