This information was found in the Compiled Service Record roll covering six Louisiana Militia, Reserve units. I did a cursory search of the records and found these men. There are undoubtedly more to be found.

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The regiment was ordered into active service June 10, 1862 to arrest deserters

Gustave Bertrand, 2nd Lieutenant, Company B, Vermillion Regiment Louisiana Militia, entered active service May 31, 1862, at Camp Pratt, La. August 14, 1862

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A. C. Perry, entered active service May 31, 1862. Reported at Camp Pratt. August 1, 1862, as Capt. Company C., Vermillion Regiment

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Joseph Pearce, 2nd Lieutenant, Company C, entered active service May 26, 1862, at Camp Pratt, La. August 14, 1862

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Ch’s W. Caldwell, Captain, Company A, reported at Camp Pratt as 4th Sergeant May 28,1862. Appointed Captain in place of S. Le Blanc, resigned. Entered into active service June 13, 1862. At Camp Pratt August 14, 1862

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N. R. Campbell, 2nd Lieutenant, Company A, Vermillion Regiment Louisiana Militia, appointed in place of Edmond Boudreauz and reporated at Camp Pratt August, 5, 1862.

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Laodice Fontelieu, 1st Lieutenant, Company A, Vermillion Regiment Louisiana Militia, appointed in place of M. Le Blanc and reported at Camp Pratt August 4, 1862.

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Dupre Guidry, 1st Lieutenant, Company B, Vermillion Regiment Louisiana Militia, entered into active service May 31, 1862, at Camp Pratt August 14, 1862.

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L. C. Rice, Captain, Company B, Vermillion Regiment Louisiana Militia, entered into active service May 24, 1862, at Camp Pratt August 14, 1862.

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M320: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Louisiana, Roll 403

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See also:

Vermillion Regiment, Louisiana Militia (Confederate)
http://www.acadiansingray.com/Vermilion%20Regt.%20Mil.htm#Vermilion%20Parish%20Regiment%20Militia