William H. Krausse is listed as enrolling in the 3rd Reg. Enrolled Missouri Militia in St. Louis on Sept 13th 1862. No mention of active service with this unit is made.
He is also listed as enlisting as a Private, Company K, Capt John G. Broemser, 41st Regiment Infantry Volunteers on Aug 27th, 1864 at Benton Barracks, St. Louis Missouri. He is listed as having "died Dec 3, 1864 in hospital St. Louis Mo and buried at Jefferson Barracks near St. Louis MO (Kreuse, Wm. H.)" I have not found a pension application or record for him which leads me to believe there was not a surviving widow.
I have not found a listing at JB National Cemetery under Krausse or Kreuse for a grave location.
The 41st was organized at Benton Barracks, Mo., August and September, 1864. Mustered in September 16, 1864. On garrison duty at St. Louis, Mo., until July, 1865. Mustered out July 11, 1865. Regiment lost during service 1 Enlisted man killed and 2 Officers and 34 Enlisted men by disease. Total 37.
A number of unit deaths occurred in December 1864. Those deaths include David Wright, Pvt Co A, 12-11-1864, John Keffer, Pvt Co C, 12-25-1864 and William Spurgeon, Pvt Co C, 6-11-1865 I mention these as all are mentioned as passing away as patients in, and buried at, the Arsenal Island Small Pox Hospital. Keffer is also listed as being interred at Jefferson Barracks.
I've not found a census listing in Missouri to match per se. The closest I've found so far is a William Krauss, born 1863 to Johann and Elisabeth Krauss located in Osage County Missouri.
Hope this helps, if you have furthe details such as a date of birth, birth origin, or parents name, I'll see what I can do.
John Russell MD