Michelle,
My interest in GWC is in his service in Bryan's Cherokee Bn. as noted in an earlier message in this thread. The following is what I have in my database on this soldier.

Crittenden, George Washington: Pvt. Co. D. Enl. 7-2-1861 for 12 mths. in Co. G, 1st Cherokee Mtd. Vols. Age 18, light complexion, light hair, dark eyes, height 5’-9.” Appears on a Co. MR dated 12-1-1861. Enl. 7-4-62 for 1 yr. by J. M. Bryan in the 1st Cherokee Partisan Rangers at Evansville, Ar. Trans. 9-13-62 to Co. D. Paid 9-30-62 by Maj. J. G. Vore. Trans. 2-3-63 to Co. H, 2nd Cherokee Mtd. Vols. upon consolidation of Adair's and Bryan's cav. battalions. Appears as "Absent without leave since June 24, 63" on 2nd Cherokee Regt. MR dated 6-30-63. B. 5-20-1844 in Cherokee Nation, son of Henry Clay Crittenden and Susannah Wolf. M.(1) Martha J. Starr. 3 children. M.(2) 3-19-1875 to Nancy Jane Wilkey. 7 children. 1880 Res. Go. Dist., CN. 1890 Res. Go. Dist., CN. Age 45. D. 4-3-1912 in Adair Co., Ok. Widow Nancy Crittenden appl. 6-21-1915 for a Conf. pension from Adair, Ok. Bur. Crittenden Cem., Westville, Ok. Brother of Henry Crittenden and Wellington Crittenden of the 1st Cherokee Mtd. Vols.
Sources:
Benge, “1880 Cherokee Nation Census, Indian Territory,” 252
Benge, “1890 Census, Cherokee Nation,” 385
CJCLDS, Family Group Record, “Henry Clay Crittenden”
“Find A Grave Memorial, George W(ashington) Crittenden.” On-line file:

http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GScid=98243&GRid=6107652
NA, CSR, 1st Cherokee Mtd. Vol’s, MF 258, Roll 79, records #362-4
NA, CSR, 2nd Cherokee Mtd. Vol's., MF 258, Roll 90, record #231
ODL, Okla. Confederate Pension Applications, Appl. #340