The most common and most likely answer to this crossword clue is the 3 plus 6 letter word NEW MEXICO
I've seen this crossword clue in Financial Times
N
E
W
M
E
X
I
C
O
More clues leading to the result NEW MEXICO
Buddy explains!

The straight part
We know that "American state" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case american state = new mexico.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.