I assume that your relative is not James P Todd. According to the Compiled Service Records, there was a James A. Todd, 22 years old that was made 2nd Corp on Oct 28, 1862 of CO K, 8th MSM Cav and died of pneumonia on Jan 8, 1863 near Lebanon. (A look at the original Company muster rolls on microfilm at the Missouri State Archives might prove the correct initial - G vs. A.)
Mary J. Todd received a widow's pension for a Private James Todd that commenced on Jan 9, 1863. There is very little info in the pension file other than the basic info and also a listing for a Sarah J. (a daughter born right after he died?) That's about all I have. As a sidenote, I do not know if a Corp pension was more than a PVT pension, but if so, your family might be owed more money - let me know if you collect it.
Craig
PS - If you don't know where your relative is buried: It appears as if Union soldiers originally buried around Lebanon were relocated after the war to Springfield National Cemetery. I could not finding a listing for your James Todd, so he might be buried as an UNKNOWN. It would take a lot of research to determine that.