What is the correct phrase to ask to determine which group a first nations person considers themselves to be part of?

You might be surprised to find out that many Native Americans don't like that politically correct name for our indiginous Americans.

Native Americans did not suffer through countless trails of tears, disease, wars, and cultural annihilation -- Indians did. The Native people today are Native Americans not Indians, therefore we do not need to feel guilty for the horrors of the past. Many Indians feel that this is what the term Native American essentially does -- it white-washes history. It cleans the slate.

So what to call them? All Things Chreokee explores this, and their recommendation:

When you don't know the specific tribe simply use the term which you are most comfortable using. The worst that can happen is that someone might correct you and open the door for a thoughtful debate on the subject of political correctness and its impact on ethnic identity. What matters in the long run is not which term is used but the intention with which it is used. ...the term "Indian" is increasingly falling back into use.

The primary division of Indian/Native American groups in the US is the Tribe.

Although increasingly, you could make a case for "Casino".

An appropriate term is "tribal affiliation"

Tribal affiliation means an association with federally recognized Indian tribes or bands.

Law insider: Tribal affiliation

... which isn't to suggest that it is always appropriate to ask.