At the battle of Corinth, Union troops reported capturing a "Louisiana flag." The only regiment at that battle was the "3rd Louisiana."

I was looking over "Google Books" and found that the 3rd Michigan Cavalry had captured the flag (a little bit after the main battle).

Source: Michigan in the war. By Michigan. Adjutant-General's Dept, Michigan Adjutant General's Office, John Robertson.

Page 475.

Hope that helps out somebody,

Have a great morning!

Shawn Prouty