Native Americans in general belong to one of five mitochondrial DNA (mtDNA) haplogroups: A, B, C, D or X and all of these are widely distributed throughout the Americas. The mtDNA is transfered from mother to daughter to grand-daughter and so on, without any influence of spouses along that line.
Likewise, paternal DNA testing, or Y-DNA, can tell if your Native heritage comes to you from your father without the influence of any spouses along that paternal line. If a female wants to know about it, she will need to have the testing done on a near male relative however, such as a brother.
Family Tree DNA will provide this information for a person testing their mtDNA or Y-DNA.