Hi, special thanks to those of you who have responded so quickly. I have found where Nancy Tate requested CC Tate's pension. It is as follows;

Confederate Pension Abstracts #8863 Pike Co., AR

C. C. Tate, Pike County Arkansas, (January 23, 1908). S.T. East and John C.C. French (Jan 23, 1908) "Well acquainted with applicant C. C. Tate and have known him 47 years, respectively." W.P. Hemby (June 8, 1912) Pike County Arkansas. "Well acquainted with C. C. Tate of Bowen (Pike County) AR. (Physicians statement). Nancy A. Tate (widow) of C. C. Tate (May 31, 1913). "My husband died January 11th, 1913." John C. C. French and Samuel T. East (May 31, 1913) citizen of Pike Co Ar. "Well acquainted with applicant's husband C.C. Tate and knew him for 50 years." Mrs. Nancy Tate died December 5, 1929. M.D. Cummings, sheriff of Pike County, Ar Public administrator. C. C. Tate served in Company K, McNeil's AR Infantry.

I still don't know the date he was on active military duty, or where he may have been stationed and what battles he may or may not have been in. I think this genealogy business should be called "Genealogy Practice", as a doctor. LOL I am still a novice even tho I have been researching for 30 plus years off and on, mostly online as I can not drive any distance to go find what's actually in the archives. I have always wanted to go to Pike Co AR, so many of my relatives are from there. Sparks, Carpenter, Tate, Starling, Cupit to name a few.
Thanks again for those of you who jumped in to help me so quickly. Perhaps with this additional information there might be more information out there. Anyone who wants to point me in a direction I would appreciate it.

Thanks!