How would I find out what Indian tribe Thomas Bickhart was from.?

First you'd determine if he WAS all or part NA.

Is this him?

1900; Census Place: Upper Augusta, Northumberland, Pennsylvania; Roll: 1450; Page: 3B; Enumeration District: 0165; FHL microfilm: 1241450

James Bickhart 31

Ida Bickhart 32

Charles F Bickhart 11

Thomas R Bickhart 8

Harry J Bickhart 6

1910; Census Place: Sunbury Ward 8, Northumberland, Pennsylvania; Roll: T624_1384; Page: 22B; Enumeration District: 0118; FHL microfilm: 1375397

James Bickhart 41

Ida P Bickhart 42

Charles F Bickhart 21

Thomas R Bickhart 18

Harry J Bickhart 15

Parry I Klinger 10

If you look at the 1910 in Oklahoma, in Cherokee County, you'll see a special appendix for Indians, with tribe and blood quantum. James and Ida don't have it in 1910.

1920; Census Place: Akron Ward 4, Summit, Ohio; Roll: T625_1439; Page: 21A; Enumeration District: 168; Image: 983

Thomas R Bickhart 26

Clare G Bickhart 19

Isabel J Bickhart 2 3/12

He (or his parents) says he is white in all four. He's in the county jail in 1930, or someone named that is. I can't tell if it is him.

https://familysearch.org/ark:/61903/1:1:M37S-T52

this is the 1900 census for Thomas R Bickhart, who was born in Aug 1891 and lives with his parents. He is listed as white. You are clearly using family story... and not any documentation. If you had used some form of documentation, you would have had a year of birth ..not "late 1800s to early 1900s".

There is no reason to believe he was from any Indian tribe.